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25 pages, 4893 KiB  
Article
A High Reliability Ferroresonant Inverter with Improved Efficiency and Wider Input Voltage
by Antony G. Theodorakis, Nikolaos S. Korakianitis, Georgios A. Vokas, George Ch. Ioannidis and Stavros D. Kaminaris
Electronics 2025, 14(1), 45; https://doi.org/10.3390/electronics14010045 - 26 Dec 2024
Viewed by 179
Abstract
In this research, a ferroresonant (SATFORMER) inverter, optimized in terms of power efficiency, noise reduction, and reliability, is analyzed and described. This modified SATFORMER inverter can be used as a standalone inverter. In the proposed topology, the variable DC input is converted to [...] Read more.
In this research, a ferroresonant (SATFORMER) inverter, optimized in terms of power efficiency, noise reduction, and reliability, is analyzed and described. This modified SATFORMER inverter can be used as a standalone inverter. In the proposed topology, the variable DC input is converted to an AC square wave by a thyristor-based modified current source inverter and additionally applied to primary winding, which is divided into four sub-windings, that are wound on the saturable core portion, via six relays with one change-over (CO) contact. The proposed ferroresonant inverter is innovative, to the best of our knowledge. A method for reducing the power losses of the proposed inverter is described and analyzed. A 150 VA model of a constant voltage transformer (ferroresonant transformer) is tested in order to experimentally investigate its basic characteristics. The circuit and simulated results of the modified current source inverter are presented in detail. The experimental results of our 150 VA model are presented. A precise term is introduced to describe the operation of the converter’s magnetic components. The occurring phenomenon is thoroughly explained, and a meaningful, perceptive, and newly incorporated term is introduced to provide a clearer understanding of the phenomenon. Full article
(This article belongs to the Special Issue Advanced Technologies in Power Electronics and Electric Drives)
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Figure 1

Figure 1
<p>Two different implementations of ferroresonant transformers: (<b>a</b>) compact type [<a href="#B29-electronics-14-00045" class="html-bibr">29</a>]; (<b>b</b>) discrete type [<a href="#B30-electronics-14-00045" class="html-bibr">30</a>].</p>
Full article ">Figure 2
<p>Complex permeability as a function of frequency of 3F3 YAGEO Ferroxcube ferrite material [<a href="#B31-electronics-14-00045" class="html-bibr">31</a>].</p>
Full article ">Figure 3
<p>(<b>a</b>) SATFORMER circuit; (<b>b</b>) B-H magnetization characteristic [<a href="#B18-electronics-14-00045" class="html-bibr">18</a>,<a href="#B19-electronics-14-00045" class="html-bibr">19</a>].</p>
Full article ">Figure 4
<p>SATFORMER schematic diagram; adopted from [<a href="#B18-electronics-14-00045" class="html-bibr">18</a>].</p>
Full article ">Figure 5
<p>SATFORMER magnetic circuit and flux distribution [<a href="#B17-electronics-14-00045" class="html-bibr">17</a>].</p>
Full article ">Figure 6
<p>SATFORMER secondary side equivalent circuit under no load conditions [<a href="#B17-electronics-14-00045" class="html-bibr">17</a>].</p>
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<p>SATFORMER secondary side equivalent circuit with a resistive load [<a href="#B17-electronics-14-00045" class="html-bibr">17</a>].</p>
Full article ">Figure 8
<p>Induced transient spikes on transmission lines that connect a remote load.</p>
Full article ">Figure 9
<p>(<b>a</b>) Proposed SATFORMER standalone inverter topology. (<b>b</b>) Magnified inverter view for clarifying.</p>
Full article ">Figure 10
<p>Smoothed square waveform of output voltage and trigger pulses.</p>
Full article ">Figure 11
<p>Experimental arrangement with the SATFORMER 150 VA.</p>
Full article ">Figure 12
<p>Output voltage waveforms of Case Study 1: (<b>a</b>) Vin = 90 V; (<b>b</b>) Vin = 130 V; (<b>c</b>) Vin = 220 V; and (<b>d</b>) Vin = 250 V.</p>
Full article ">Figure 13
<p>Output voltage waveforms of Case Study 2: (<b>a</b>) Vin = 90 V; (<b>b</b>) Vin = 130 V; (<b>c</b>) Vin = 220 V; and (<b>d</b>) Vin = 250 V.</p>
Full article ">Figure 13 Cont.
<p>Output voltage waveforms of Case Study 2: (<b>a</b>) Vin = 90 V; (<b>b</b>) Vin = 130 V; (<b>c</b>) Vin = 220 V; and (<b>d</b>) Vin = 250 V.</p>
Full article ">Figure 14
<p>Output voltage waveforms of Case Study 3: (<b>a</b>) Vin = 90 V; (<b>b</b>) Vin = 130 V; (<b>c</b>) Vin = 220 V; and (<b>d</b>) Vin = 250 V.</p>
Full article ">Figure 15
<p>Output voltage waveforms of Case Study 4: (<b>a</b>) Vin = 90 V; (<b>b</b>) Vin = 130 V; (<b>c</b>) Vin = 220 V; and (<b>d</b>) Vin = 250 V.</p>
Full article ">Figure 16
<p>The aggregated graph of the output voltage versus the input voltage of the case studies.</p>
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14 pages, 2541 KiB  
Article
Magnetoelastic Effect in Ni-Zn Ferrite Under Torque Operation
by Jacek Salach, Maciej Kachniarz, Dorota Jackiewicz and Adam Bieńkowski
Materials 2024, 17(24), 6239; https://doi.org/10.3390/ma17246239 - 20 Dec 2024
Viewed by 242
Abstract
The magnetoelastic effect is known as the dependence between the magnetic properties of the material and applied mechanical stress. The stress might not be applied directly but rather generated by the applied torque. This creates the possibility of developing a torque-sensing device based [...] Read more.
The magnetoelastic effect is known as the dependence between the magnetic properties of the material and applied mechanical stress. The stress might not be applied directly but rather generated by the applied torque. This creates the possibility of developing a torque-sensing device based on the magnetoelastic effect. In this paper, the concept of an axially twisted toroidal magnetic core as a torque-sensing element is considered. Most known works in this field consider the utilization of an amorphous ribbon as the core material. However, Ni-Zn ferrites, exhibiting relatively high magnetostriction, also seem to be promising materials for magnetoelastic torque sensors. This paper introduces a theoretical description of the magnetoelastic effect under torque operation on the basis of total free energy analysis. The methodology of torque application to the toroidal core, utilized previously for coiled cores of amorphous ribbons, was successfully adapted for the bulk ferrite core. For the first time, the influence of torque on the magnetic properties of Ni-Zn ferrite was investigated in a wide range of magnetizing fields. The obtained magnetoelastic characteristics allowed the specification of the magnetoelastic torque sensitivity of the material and the determination of the optimal amplitude of the magnetizing field to maximize this parameter. High sensitivity, in comparison with previously studied amorphous alloys, and monotonic magnetoelastic characteristics indicate that the investigated Ni-Zn ferrite can be utilized in magnetoelastic torque sensors. As such, it can be used in torque-sensing applications required in mechanical engineering or civil engineering, like the evaluation of structural elements exposed to torsion. Full article
(This article belongs to the Collection Magnetoelastic Materials)
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Figure 1

Figure 1
<p>Influence of the axial stress <math display="inline"><semantics> <mi>σ</mi> </semantics></math> on the normalized maximum magnetic flux density <math display="inline"><semantics> <msub> <mi>B</mi> <mi>m</mi> </msub> </semantics></math> for the material with positive (<math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>s</mi> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, solid green line) and negative (<math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>s</mi> </msub> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>, dashed red line) magnetostriction [<a href="#B25-materials-17-06239" class="html-bibr">25</a>,<a href="#B28-materials-17-06239" class="html-bibr">28</a>,<a href="#B31-materials-17-06239" class="html-bibr">31</a>].</p>
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<p>Schematic representation of the stress state of toroidal core subjected to the axial torque <math display="inline"><semantics> <msub> <mi>M</mi> <mi>τ</mi> </msub> </semantics></math>. For the pure torsion, shear stress <math display="inline"><semantics> <mi>τ</mi> </semantics></math> in elementary excerpt can be decomposed into the pair of principal stress of value equal to <math display="inline"><semantics> <mi>τ</mi> </semantics></math>: <math display="inline"><semantics> <mrow> <mo>+</mo> <mi>σ</mi> <mo>=</mo> <mo>|</mo> <mo>−</mo> <mi>σ</mi> <mo>|</mo> <mo>=</mo> <mi>τ</mi> </mrow> </semantics></math> [<a href="#B31-materials-17-06239" class="html-bibr">31</a>].</p>
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<p>Schematic block diagram of the measurement system: <span class="html-italic">H</span>—magnetizing field, <span class="html-italic">B</span>—magnetic flux density, <math display="inline"><semantics> <msub> <mi>M</mi> <mi>τ</mi> </msub> </semantics></math>—torque.</p>
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<p>Application of the axial torque <math display="inline"><semantics> <msub> <mi>M</mi> <mi>τ</mi> </msub> </semantics></math> to the toroidal core magnetized along perimeter with the field <span class="html-italic">H</span>: 1—Ni-Zn ferrite core, 2—epoxy resin mold, 3—non-magnetic brass clutch (3a—beam, 3b—stem), 4—magnetizing coil, 5—sensing coil.</p>
Full article ">Figure 5
<p>Influence of the applied torque <math display="inline"><semantics> <msub> <mi>M</mi> <mi>τ</mi> </msub> </semantics></math> on the magnetization characteristics <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo> </mrow> </semantics></math> of investigated Ni-Zn ferrite for the magnetizing field amplitude: (<b>a</b>) <math display="inline"><semantics> <msub> <mi>H</mi> <mi>m</mi> </msub> </semantics></math> = 5 A/m (the Rayleigh region), (<b>b</b>) <math display="inline"><semantics> <msub> <mi>H</mi> <mi>m</mi> </msub> </semantics></math> = 15 A/m (the high permeability region), (<b>c</b>) <math display="inline"><semantics> <msub> <mi>H</mi> <mi>m</mi> </msub> </semantics></math> = 100 A/m (the saturation region).</p>
Full article ">Figure 6
<p>The selected magnetoelastic characteristics <math display="inline"><semantics> <mrow> <msub> <mi>B</mi> <mi>m</mi> </msub> <msub> <mrow> <mo>(</mo> <msub> <mi>M</mi> <mi>τ</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>H</mi> <mi>m</mi> </msub> </msub> </mrow> </semantics></math> of investigated Ni-Zn ferrite: (<b>a</b>) for lower magnetizing field amplitudes <span class="html-italic">H<sub>m</sub></span> ≤ 10 A/m, (<b>b</b>) for higher magnetizing field amplitudes <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mi>m</mi> </msub> <mo>&gt;</mo> </mrow> </semantics></math> 10 A/m: <math display="inline"><semantics> <msub> <mi>H</mi> <mi>m</mi> </msub> </semantics></math> = 2.5–7.5 A/m—the Rayleigh region, <math display="inline"><semantics> <msub> <mi>H</mi> <mi>m</mi> </msub> </semantics></math> = 10–25 A/m—the high permeability region, <math display="inline"><semantics> <msub> <mi>H</mi> <mi>m</mi> </msub> </semantics></math> = 50–100 A/m—the saturation region.</p>
Full article ">Figure 7
<p>Dependence of the magnetoelastic torque sensitivity <math display="inline"><semantics> <msub> <mi>S</mi> <mi>M</mi> </msub> </semantics></math> of the investigated Ni-Zn ferrite on the magnetizing field amplitude <math display="inline"><semantics> <msub> <mi>H</mi> <mi>m</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>M</mi> <mi>τ</mi> </msub> </mrow> </semantics></math> = 6.05 Nm.</p>
Full article ">
8 pages, 2806 KiB  
Article
Observation of Zigzag-Shaped Magnetic Domain Boundaries in Granular Perpendicular Magnetic Recording Media Using Alternating Magnetic Force Microscopy
by M. V. Makarova, Hanamichi Tanaka, Hiroshi Sonobe, Toru Matsumura and Hitoshi Saito
Magnetochemistry 2024, 10(12), 106; https://doi.org/10.3390/magnetochemistry10120106 - 13 Dec 2024
Viewed by 445
Abstract
In granular media for perpendicular magnetic recording, zigzag-shaped magnetic domain boundaries form between magnetic grains isolated by a non-magnetic grain boundary phase. They are the main source of jitter noise caused by the position fluctuation of magnetic bit transitions. The imaging of zigzag [...] Read more.
In granular media for perpendicular magnetic recording, zigzag-shaped magnetic domain boundaries form between magnetic grains isolated by a non-magnetic grain boundary phase. They are the main source of jitter noise caused by the position fluctuation of magnetic bit transitions. The imaging of zigzag boundaries thus becomes an important task to increase recording density with decreasing bit size, when the zigzag and bit sizes become comparable. We visualized the zigzag boundaries of magnetic domains in as-sputtered granular media with a spatial resolution of less than 3 nm using our developed Alternating Magnetic Force Microscopy (A-MFM). We used a soft magnetic amorphous FeCoB tip with high saturation magnetization, which further enhances the spatial resolution through the inverse magnetostrictive effect. The zigzag size ranged from 2 to 8 nm in media with an estimated grain size of around 5 nm. Additionally, we observed zigzag bit boundaries in commercially recorded granular media with a recording density of 500 kfci. Full article
(This article belongs to the Section Magnetic Nanospecies)
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Figure 1
<p>Diagram of the pyramidal Si tip with a soft magnetic amorphous FeCoB coating (<b>a</b>) and the experimental setup (<b>b</b>).</p>
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<p>128 × 128 px A-MFM images of topography (<b>a</b>,<b>d</b>) and <span class="html-italic">X</span> in-phase out-of-plane signal <math display="inline"><semantics> <mrow> <msubsup> <mi>m</mi> <mi>z</mi> <mrow> <mi>a</mi> <mi>c</mi> </mrow> </msubsup> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msup> <mo>∂</mo> <mn>2</mn> </msup> <msubsup> <mi>H</mi> <mi>z</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msubsup> </mrow> <mrow> <mo>∂</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mstyle> </mrow> </semantics></math> (<b>b</b>,<b>e</b>) for granular media with (<b>a</b>–<b>c</b>) coarse and (<b>d</b>–<b>f</b>) fine grain sizes. The corresponding pixel view with a magnified area of the zero transition line: (<b>c</b>) for coarse and (<b>f</b>) for fine media. Yellow circles indicate the evaluated average grain size.</p>
Full article ">Figure 3
<p>128 × 128 px images of zero transition lines obtained from the <span class="html-italic">X</span> in-phase out-of-plane signal for coarse (<b>a</b>) and fine (<b>b</b>) granular sizes. The lines are approximated by segmented straight lines. (<b>c</b>) Histograms of zigzag lengths obtained from those lines. One pixel is 2.5 nm.</p>
Full article ">Figure 4
<p>(<b>a</b>) Optimized A-MFM image of perpendicular magnetic recording media with a 500 kfci recording density. (<b>b</b>) 3D image of the magnetic signal <math display="inline"><semantics> <mrow> <msubsup> <mi>m</mi> <mi>z</mi> <mrow> <mi>a</mi> <mi>c</mi> </mrow> </msubsup> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msup> <mo>∂</mo> <mn>2</mn> </msup> <msubsup> <mi>H</mi> <mi>z</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msubsup> </mrow> <mrow> <mo>∂</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mstyle> </mrow> </semantics></math> vs (<span class="html-italic">x,y</span>) coordinates. (<b>c</b>–<b>e</b>) Magnetic transition boundaries obtained with a range of thresholds for zero crossing <span class="html-italic">d</span> in % of the difference between the maximum and minimum signal values. <span class="html-italic">d</span> values are 0, 1 and 2% for (<b>c</b>–<b>e</b>) figures, respectively.</p>
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<p>Power spectrum image corresponding to <a href="#magnetochemistry-10-00106-f004" class="html-fig">Figure 4</a>a. The onset point is shown for the calculation of the maximum wavenumber <span class="html-italic">k<sub>x</sub></span> and the minimum wavelength.</p>
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24 pages, 6146 KiB  
Article
On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment
by Nicolae Herisanu, Bogdan Marinca and Vasile Marinca
Mathematics 2024, 12(23), 3836; https://doi.org/10.3390/math12233836 - 4 Dec 2024
Viewed by 430
Abstract
The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the [...] Read more.
The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the nonlinear differential equations were obtained for the pinned–pinned boundary conditions with the help of the Galerkin–Bubnov procedure and Hamiltonian approach. The nonlinear differential equations were studied using an original, explicit, and very efficient technique, namely the optimal auxiliary functions method (OAFM). It should be emphasized that our procedure assures a rapid convergence of the approximate analytical solutions after only one iteration, without the presence of a small parameter in the governing equations or boundary conditions. Detailed results are presented on the effects of some parameters, among them being analyzed were the damping, frequency, electromagnetic, and nonlinear elastic foundation coefficients. The local stability of the equilibrium points was performed by introducing two variable expansion method, the homotopy perturbation method, and then applying the Routh–Hurwitz criteria and eigenvalues of the Jacobian matrix. Full article
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Figure 1

Figure 1
<p>Geometric and coordinate of laminated composite beam with magnetostrictive layer, electromagnetic actuator, mechanical impact, and elastic foundation.</p>
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<p>Comparison between the analytical and numerical results, <b><span style="color:red">____</span></b> numerical <b><span style="color:blue">_ _ _</span></b> analytical: (<b>a</b>) comparison for <span class="html-italic">T</span><sub>1</sub>; (<b>b</b>) comparison for <span class="html-italic">T</span><sub>2</sub>.</p>
Full article ">Figure 3
<p>The effects of parameter <span class="html-italic">μ</span><sub>1</sub>: <span class="html-italic">μ</span><sub>1</sub> = 0.0027 (blue), <span class="html-italic">μ</span><sub>2</sub> = 0.0054 (red), <span class="html-italic">μ</span><sub>3</sub> = 0.0081 (green): (<b>a</b>) effect on <span class="html-italic">T</span><sub>1</sub>; (<b>b</b>) effect on <span class="html-italic">T</span><sub>2</sub>.</p>
Full article ">Figure 4
<p>The effects of parameter <span class="html-italic">ω</span>: <span class="html-italic">ω</span> = 0.5 (blue), ω = 0.6 (red), ω = 0.7 (green): (<b>a</b>) effect on T<sub>1</sub>; (<b>b</b>) effect on T<sub>2</sub>.</p>
Full article ">Figure 5
<p>The effects of parameter <span class="html-italic">m</span><sub>1</sub>: <span class="html-italic">m</span><sub>1</sub> = 0.009 (blue), <span class="html-italic">m</span><sub>1</sub> = 0.09 (red), <span class="html-italic">m</span><sub>1</sub> = 0.9 (green): (<b>a</b>) effect on <span class="html-italic">T</span><sub>1</sub>; (<b>b</b>) effect on <span class="html-italic">T</span><sub>2</sub>.</p>
Full article ">Figure 6
<p>The effects of parameter <span class="html-italic">m</span><sub>2</sub>: <span class="html-italic">m</span><sub>2</sub> = 0.812 (blue), <span class="html-italic">m</span><sub>2</sub> = 0.08 (red), <span class="html-italic">m</span><sub>2</sub> = 0.008 (green): (<b>a</b>) effect on <span class="html-italic">T</span><sub>1</sub>; (<b>b</b>) effect on <span class="html-italic">T</span><sub>2</sub>.</p>
Full article ">Figure 7
<p>The effects of parameter <span class="html-italic">m</span><sub>13</sub>: <span class="html-italic">m</span><sub>13</sub> = 0.041 (blue), <span class="html-italic">m</span><sub>13</sub> = 0.4 (red), <span class="html-italic">m</span><sub>13</sub> = 1.4 (green): (<b>a</b>) effect on <span class="html-italic">T</span><sub>1</sub>; (<b>b</b>) effect on <span class="html-italic">T</span><sub>2</sub>.</p>
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<p>The effects of parameter <span class="html-italic">h</span><sub>1</sub>: <span class="html-italic">h</span><sub>1</sub> = 0.0095 (blue), <span class="html-italic">h</span><sub>1</sub> = 0.095 (red), <span class="html-italic">h</span><sub>1</sub> = 0.95 (green): (<b>a</b>) effect on <span class="html-italic">T</span><sub>1</sub>; (<b>b</b>) effect on <span class="html-italic">T</span><sub>2</sub>.</p>
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<p>Variation of parameter Λ with the coefficients given in <a href="#sec5-mathematics-12-03836" class="html-sec">Section 5</a>.</p>
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<p>Variation of the equilibrium points: (<b>a</b>) <span class="html-italic">A</span><sub>3e</sub>; (<b>b</b>) <span class="html-italic">A</span><sub>4e</sub>.</p>
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<p>Variation of <span class="html-italic">tr</span>[<span class="html-italic">J</span>] for Λ = 0.5 (blue), Λ = 1 (red), and Λ = 1.25 (green).</p>
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<p>Variation of det[<span class="html-italic">J</span>] for Λ = 0.5 (blue), Λ = 1 (red), and Λ = 1.25 (green).</p>
Full article ">
61 pages, 20006 KiB  
Review
Magnetoelectric BAW and SAW Devices: A Review
by Bin Luo, Prasanth Velvaluri, Yisi Liu and Nian-Xiang Sun
Micromachines 2024, 15(12), 1471; https://doi.org/10.3390/mi15121471 - 3 Dec 2024
Viewed by 712
Abstract
Magnetoelectric (ME) devices combining piezoelectric and magnetostrictive materials have emerged as powerful tools to miniaturize and enhance sensing and communication technologies. This paper examines recent developments in bulk acoustic wave (BAW) and surface acoustic wave (SAW) ME devices, which demonstrate unique capabilities in [...] Read more.
Magnetoelectric (ME) devices combining piezoelectric and magnetostrictive materials have emerged as powerful tools to miniaturize and enhance sensing and communication technologies. This paper examines recent developments in bulk acoustic wave (BAW) and surface acoustic wave (SAW) ME devices, which demonstrate unique capabilities in ultra-sensitive magnetic sensing, compact antennas, and quantum applications. Leveraging the mechanical resonance of BAW and SAW modes, ME sensors achieve the femto- to pico-Tesla sensitivity ideal for biomedical applications, while ME antennas, operating at acoustic resonance, allow significant size reduction, with high radiation gain and efficiency, which is suited for bandwidth-restricted applications. In addition, ME non-reciprocal magnetoacoustic devices using hybrid magnetoacoustic waves present novel solutions for RF isolation, which have also shown potential for the efficient control of quantum defects, such as negatively charged nitrogen-vacancy (NV) centers. Continued advancements in materials and device structures are expected to further enhance ME device performance, positioning them as key components in future bio-sensing, wireless communication, and quantum information technologies. Full article
(This article belongs to the Special Issue Novel Surface and Bulk Acoustic Wave Devices)
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Figure 1

Figure 1
<p>Magnetoelectric (ME) device possibilities using BAW and SAW concepts. The ME devices include magnetic sensors, antennas, isolators, and filters.</p>
Full article ">Figure 2
<p>(<b>a</b>) Schematic diagram of the Metglas/piezo fiber ME sensor configuration, featuring ID electrodes on the PMN-PT fiber core composite and symmetric three-layer Metglas actuators. (<b>b</b>) Exploded view of individual components. (<b>c</b>) Illustration of multiple alternating push–pull units for enhanced ME coupling. (<b>d</b>) Optical microscopy image of a longitudinally poled push–pull element within the core composite. (<b>e</b>) Photographs of the fully assembled Metglas/piezo fiber ME sensor. Reproduced with permission from Refs. [<a href="#B17-micromachines-15-01471" class="html-bibr">17</a>,<a href="#B64-micromachines-15-01471" class="html-bibr">64</a>]. Copyright 2021 IEEE; Copyright 2011 John Wiley and Sons.</p>
Full article ">Figure 3
<p>(<b>a</b>) Process flow of cantilever-based ME sensors. (<b>b</b>) Bonding process flow of capped wafer to effectively improve the mechanical quality factor and reduce the equivalent magnetic noise. (<b>c</b>) Photographs of ME sensor die on wafer (<b>d</b>) cantilever-based ME sensor with (1) ME cantilever, (2) etch groove, (3) bond frame, and (4) bond pads. Reprinted with permission from Ref. [<a href="#B222-micromachines-15-01471" class="html-bibr">222</a>]. Copyright Elsevier 2013.</p>
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<p>Magnetically modulated cantilever ME sensor with antiparallel exchange bias (APEB) stack. (<b>a</b>) The sketch illustrates the ME cantilever design with the magnetic field sensing axis indicated. A cross-sectional view highlights the ME sensor’s structure, showing the Si substrate, a piezoelectric AlN layer, a Pt and Au electrode, and the magnetostrictive layer. The magnetostrictive layer consists of a repeated multilayer structure with Ta/Cu seed layers, an antiferromagnetic MnIr layer, and a magnetostrictive FeCoSiB phase. This structure includes a 20× repeated two-layer configuration. Key magnetic parameters are indicated, including the uniaxial anisotropy axis K<sub>u</sub>, the exchange bias field H<sub>eb</sub>, and the magnetic stray field distribution H<sub>stray</sub>. (<b>b</b>) A diagram shows the temporal application of temperature and magnetic field during the annealing process. (<b>c</b>) An inductive measurement shows the magnetization loop along the alternating EB axis, with a magnetization loop from a parallel exchange-biased (PEB) sample included for comparison. (<b>d</b>) Magnetic domain (MD) structures at 300 °C after demagnetizing the sensor and achieving a stabilized magnetization state at room temperature (RT) for the APEB sensor. The alignment of magnetization M, the EB field H<sub>eb</sub> in the top layer, the sensor’s magnetic field sensing axis, and the magneto-optical sensitivity (MO) axis are depicted. Reprinted with permission from Ref. [<a href="#B181-micromachines-15-01471" class="html-bibr">181</a>]. Copyright 2019 AIP Publishing.</p>
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<p>Magnetic domain behavior and noise performance of magnetically modulated cantilever ME sensor with antiparallel exchange bias (APEB) stack and PEB stack. (<b>a</b>) A full-sensor view of the APEB’s magnetic domain structure, with magnetization directions marked by arrows. (<b>c</b>) A full-sensor view for the PEB sensor, highlighting differences in magnetic domain patterns compared to APEB. (<b>b</b>,<b>d</b>) Provide high-resolution domain images of specific regions at the right cantilever edge (indicated by red dashed boxes in (<b>a</b>,<b>c</b>)) for both APEB and PEB, respectively, illustrating domain behavior with and without an applied magnetic field. Dashed arrows denote the magnetization alignment in the second, non-visible FeCoSiB layer. (<b>e</b>) The magnetoelectric (ME) coefficient α<sub>ME</sub> changes with bias field H<sub>bias</sub> at the mechanical resonance frequency f<sub>res</sub>. (<b>f</b>) Frequency spectra of voltage noise density V<sub>ME</sub> for both APEB and PEB sensors under the same modulation H<sub>mod</sub> and signal fields H<sub>sig</sub>. (<b>g</b>) Voltage noise dependency on H<sub>mod</sub>, highlighting the sensitivity to modulation field strength. (<b>h</b>) and (<b>i</b>) show linearity plots of f<sub>res</sub> and magnetic frequency conversion (MFC) mode for a ME sensor with APEB and PEB phases, respectively. Noise floors and optimal H<sub>bias</sub> and H<sub>mod</sub> values for resonance and MFC modes are indicated, showing comparative sensor performance across configurations. Reproduced with permission from Ref. [<a href="#B181-micromachines-15-01471" class="html-bibr">181</a>]. Copyright 2019 AIP Publishing.</p>
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<p>Electrically modulated ME sensors with AlN layer for voltage output. (<b>a</b>) The schematic shows a magnetoelectric (ME) composite sample with three active layers: an exchange-biased FeCoSiB layer serving as the magnetostrictive phase, an AlN layer as the linear piezoelectric phase for readout, and an unpoled PZT layer as the nonlinear piezoelectric phase for excitation. (<b>b</b>) Displacement–voltage characteristic curve of the ME cantilever showing responses of both piezoelectric phases under a DC electric field. (<b>c</b>) The sensor output spectrum from the AlN layer when the PZT layer is excited at its mechanical resonance frequency of <span class="html-italic">f</span><sub>mod</sub> = 689 Hz. (<b>d</b>) Sensor output spectrum from the AlN layer with the carrier signal frequency <span class="html-italic">f</span><sub>res</sub> = <span class="html-italic">f</span><sub>mod</sub> = 669 Hz, applied at 20 Hz below the mechanical resonance. (<b>e</b>) A linearity test under a 10 Hz magnetic field demonstrates that the noise floor reaches approximately 10 nT/√Hz. Reproduced with permission from Ref. [<a href="#B11-micromachines-15-01471" class="html-bibr">11</a>]. Copyright 2016 AIP Publishing.</p>
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<p>Electrically modulated U-mode ME sensors with a picking-up coil for voltage output. (<b>a</b>) Schematic setup: a composite, embedded in a pickup coil, is shown. The piezoelectric (PE) plate capacitor functions as the input, while the tuned pickup coil, coupled with an amplifier, provides the output signal. (<b>b</b>) Circuit representation: the ME composite is modeled as a radiative capacitor. The pickup coil generates a signal that is buffered by a low-noise, unity-gain buffer amplifier, enhancing signal integrity. (<b>c</b>) Frequency response analysis: the self-resonant frequency of the pickup coil (with quality factor Q∼150) and the mechanical resonance frequency (with quality factor Q∼1000, labeled as UM) are shown. Tuning the system maximizes voltage output at resonance, with de-tuning options also analyzed. (<b>d</b>) Wide frequency response: a broad response shows coil resonance effects and two distinct voltage peaks correspond to mechanical resonances of the system. (<b>e</b>) MOKE microscopy image: the full cantilever length is captured after magnetic field decay, showing magnetization along the thermally induced magnetic easy axis (K<sub>u</sub>). Applied magnetic fields (H) align with the hard axis, while the left end of the cantilever is fixed to the PCB. (<b>f</b>) Vibrometry measurements showing the U-mode at 514.8 kHz. (<b>g</b>) Sensitivity at zero field showing a linear increase with rising carrier voltage amplitude. (<b>h</b>) Voltage noise characteristics versus carrier amplitude. At low frequencies (&lt;20 Hz), two regimes are identified based on carrier amplitude. Below 200 mV, noise increases only slightly, while above 200 mV, noise surges by nearly seven times for an additional 100 mV of excitation. Inset shows the noise spectra for 80 mV and 220 mV cases; the 220 mV excitation exhibits a noticeable pedestal and increased broadband noise. (<b>i</b>) LOD is assessed across different test frequencies, showing an exponential noise increase towards the carrier, which limits sensor performance. Reproduced from Ref. [<a href="#B10-micromachines-15-01471" class="html-bibr">10</a>].</p>
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<p>Low-noise inverse ME sensor based on electrically modulated U mode and exchange bias stack with a pickup coil. (<b>a</b>) Schematic of cantilever sensors in the inverse magnetoelectric configuration, featuring a simplified pickup coil covering the cantilever’s entire free length except where it connects to the circuit board. The measurement and bias field directions are shown by the blue arrow, while the orange arrow indicates the magnetic field direction applied during annealing. (<b>b</b>) Finite Element Method (FEM)-derived deflection of the cantilever in the U mode, depicted with amplified amplitude to illustrate bending. (<b>c</b>) Diagram of the advanced layer stack design for magnetic flux closure, showing Ta/Cu/MnIr layers, with each exchange-coupled to a FeCoSiB layer. The arrows represent potential magnetic flux closure and the preferred magnetization direction without cantilever excitation. (<b>d</b>) BH-Looper hysteresis curves for heat-treated single-layer (SL) and multi-layer (ML) samples (8 × 500 nm exchange bias layers) measured along the cantilever’s long axis, both with a total FeCoSiB thickness of 4 μm. (<b>e</b>) Magneto-optical Kerr micrographs of demagnetized domain patterns in SL and ML samples along the long axis, with sensitivity axis oriented along the cantilever’s short side. (<b>f</b>) Sideband amplitude response at several magnetic test signal amplitudes at 10 Hz, demonstrating extended linear behavior. (<b>g</b>) Equivalent magnetic noise density with limit of detection (LOD) calculated at 10 Hz (blue), 33 Hz (black), and 70 Hz (green), showing noise reduction and improved LOD at higher frequencies with a constant sensitivity of 85 kV/T across test fields from 10 to 70 Hz. Reproduced from Ref. [<a href="#B13-micromachines-15-01471" class="html-bibr">13</a>].</p>
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<p>Multimode delta-E effect magnetic field sensors with adapted electrodes. (<b>a</b>) Schematic cross-section of the cantilever beam, (<b>b</b>) top view of the cantilever showing the various electrode designs, (<b>c</b>) calculated deflection of the cantilever in the first and second transverse bending modes according to Euler–Bernoulli beam theory, and (<b>d</b>) photograph of the sensing cantilever mounted within a silicon frame. Effective noise level for the (<b>e</b>) first and (<b>f</b>) second modes. Reproduced with permission from Ref. [<a href="#B221-micromachines-15-01471" class="html-bibr">221</a>]. Copyright 2016 AIP Publishing.</p>
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<p>(<b>a</b>) Schematic and (<b>b</b>) layered structure of the ME sensor. Scanning electron microscopy images of the (<b>c</b>) fabricated MEMS ME sensor and the (<b>d</b>) cross-section. Reproduced from Ref. [<a href="#B180-micromachines-15-01471" class="html-bibr">180</a>].</p>
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<p>(<b>a</b>) MBVD model fitting for admittance curve of the ME sensor. (<b>b</b>) The equivalent MBVD circuit of the ME resonator. (<b>c</b>) Admittance curves of the ME resonator under different DC bias magnetic fields. (<b>d</b>) EMR frequency and peak admittance amplitude at the resonance frequency versus DC magnetic fields. Reproduced from Ref. [<a href="#B180-micromachines-15-01471" class="html-bibr">180</a>].</p>
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<p>Self-biased NPR array dual-band ME sensor/antenna. (<b>a</b>) A 3D schematic of the ME sensor/antenna. (<b>b</b>) Optical image of a fabricated smart ME antenna. (<b>c</b>) Power spectrum of the reflected signal from the ME antenna after demodulation and lowpass filtering. (<b>d</b>) Zoom-in modulation signal at 1 kHz. (<b>e</b>) Modulated voltage as a function of modulated signal magnetic flux density, showing a 470 pT LOD. (<b>f</b>) LOD as a function of modulation signal frequency. (<b>g</b>) Power transfer efficiency as a function of distance between transmission and receiving antennas. Reproduced from Ref. [<a href="#B14-micromachines-15-01471" class="html-bibr">14</a>].</p>
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<p>(<b>a</b>) Schematic of the wideband SAW-based magnetic sensor. The sensor is built on a ST–cut quartz substrate, with SiO<sub>2</sub> guiding layer, and FeCoBSi as a sensing layer. (<b>b</b>) The image shows the frequency vs. amplitude density. The authors report a LOD of 80 pT/Hz<sup>1/2</sup> at 100 Hz, a bandwidth of 50 kHz, and a dynamic range of 120 dB. Reprinted from Ref. [<a href="#B22-micromachines-15-01471" class="html-bibr">22</a>].</p>
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<p>(<b>a</b>) The illustration of a Love-Wave-based magnetic sensor based on a ST–cut quartz substrate. (<b>b</b>) The magnetization loops of different configurations of stacks. Note that the one deposited under the in-situ field has low anisotropy (red) compared to the one with post annealing after film deposition (blue). (<b>c</b>) The measured sensitivity as a function of the applied DC bias field for the configuration deposited with in-situ magnetic field. (<b>d</b>) LOD as a function of frequency for different magnetic orientation configurations. The lowest LOD is from the device with the magnetic stack deposited with an in situ magnetic field. Reprinted with permission from Ref. [<a href="#B23-micromachines-15-01471" class="html-bibr">23</a>]. Copyright 2020 AIP Publishing.</p>
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<p>(<b>a</b>) The SAW sensor design consisting of a ST–cut quartz substrate, a SiO<sub>2</sub> guiding layer and an anti-parallel exchange biased magnetostrictive layer (for sensing). (<b>b</b>) The layer stack of the magnetostrictive layer; it consists of two layers (Ta/FeCoSiB/NiFe/MnIr/Ta) that are antiparallel to each other. The NiFe/MnIr induces the exchange bias in the FeCoSiB layers of. (<b>c</b>) The magneto-optical Kerr effect microscope images from the top on a single FeCoSiB layer and a two-layer anti-parallel exchange bias stack. The image clearly shows the significant reduction in the domain wall density. (<b>d</b>) LOD plotted as a function of excitation power at 10 Hz and 100 Hz. Note that the LOD has the lowest value at 5 dBm for both frequencies. (<b>e</b>) Frequency spectrum of LOD with 5 dBm power. The LOD decreases as frequency increases, and an impressive LOD below 5 pT/Hz<sup>1/2</sup> is achieved at 1 kHz. Reprinted from Ref. [<a href="#B25-micromachines-15-01471" class="html-bibr">25</a>].</p>
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<p>(<b>a</b>) The illustration of the NPR antenna and the measurement setup. The high-frequency magnetic field is generated by the RF coil. On the bottom, a SEM picture of the antenna is shown with different individual layers (AlN, FeGaB, and Au). (<b>b</b>) The admittance curve and the Butterworth–van Dyke mode, and the inset shows the various parameters. (<b>c</b>) Admittance curve of a control device, where the magnetic layer is replaced with Cu. (<b>d</b>) The ME coefficient (right) and ME-induced voltage in the piezoelectric layer as a function of frequency. (<b>e</b>) Analog-induced voltage in the piezoelectric layer of the control device; the inset shows a zoomed-in view of the red circle. (<b>f</b>) The set-up of a FBAR antenna that uses a horn antenna to excite the magnetostrictive layer. At the bottom, a SEM picture of the close-up of the FBAR antenna highlighting the individual layers (AlN, FeGaB, and Au). (<b>g</b>) Return loss curve (S<sub>22</sub>) of the ME FBAR antenna. The inset shows the simulated displacement of the ME FBAR device at resonance. (<b>h</b>) Return loss curve (S<sub>22</sub>) of the control FBAR device when the magnetic layer is replaced with a non-magnetic Al layer. (<b>i</b>) The transmission (S<sub>12</sub>) and receiving (S<sub>21</sub>) behavior of the FBAR antenna. (<b>j</b>) Transmission (S<sub>12</sub>) and receiving (S<sub>21</sub>) curves of the control FBAR device; note the sharp reduction of the peaks compared to the ME FBAR. Reprinted from Ref. [<a href="#B15-micromachines-15-01471" class="html-bibr">15</a>].</p>
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<p>(<b>a</b>) Return loss curve (S<sub>11</sub>) of the ME FBAR antenna with a resonant frequency of 1.95 GHz and an 8.4 MHz bandwidth mounted on different sizes of ground planes (GP1–GP5). (<b>b</b>) Transmission (S<sub>21</sub>) curves of the ME FBAR antennas along with a control device (mounted on top of a 2 cm × 2 cm plastic substrate). Note the 3 dB gain enhancement of the ME FBAR mounted on GP vs. control device. (<b>c</b>) Optical images of four ME FBAR antenna array configurations. (<b>d</b>) Gain enhancement of different antenna configurations, showing a non-linear increase in gain as a function of antenna number. Reprinted from Ref. [<a href="#B19-micromachines-15-01471" class="html-bibr">19</a>].</p>
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<p>(<b>a</b>) Cross-sectional view of the SMR ME antenna showing the different layers. The Bragg reflector (3 × W/SiO<sub>2</sub>), Pt (bottom electrode), ZnO, and FeGaB layers are evident. (<b>b</b>) Optical image of the SMR ME antenna. The GSG pads are used to feed the signal during transmission mode or read out the signal in the receiving mode of the antenna. (<b>c</b>) The power-handling capability of the SMR ME antenna compared to the FBAR ME antenna. The SMR has a 1 dB compression point at 30.4 dBm while the FBAR has it at 7.1 dBm. Reprinted from Ref. [<a href="#B20-micromachines-15-01471" class="html-bibr">20</a>].</p>
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<p>(<b>a</b>) The illustration of the SAW-based ME antenna showing different layer configurations. (<b>b</b>) The optical image of the SAW-based ME antenna. (<b>c</b>,<b>d</b>) Device testing schematic and the associated radiation pattern of the SAW ME antenna. Reprinted with permission from Ref. [<a href="#B261-micromachines-15-01471" class="html-bibr">261</a>]. Copyright 2024 IEEE.</p>
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<p>The VLF ME antenna: (<b>a</b>) A 3D model showing each layer. (<b>b</b>) An optical top view photograph with the antenna’s dimensions. (<b>c</b>) The measured received signal at the resonance frequency along with the noise floor. (<b>d</b>) The measured output voltage as the bias field decreases, showing the limit of detection. (<b>e</b>) Predicted and measured magnetic field distribution as a function of distance. (<b>f</b>) Radiation field and power consumption of the ME transmitter under varying driving voltages. Reprinted with permission from Ref. [<a href="#B263-micromachines-15-01471" class="html-bibr">263</a>]. Copyright 2020 IEEE.</p>
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<p>Experimental results on the giant nonreciprocity effect of hybridized SAW/SW in the FeGaB/Al<sub>2</sub>O<sub>3</sub>/FeGaB multilayer stack on the piezoelectric lithium niobate substrate at the frequency of 1435 MHz when a growth field (<span class="html-italic">H<sub>G</sub></span>) was oriented at 60°. Acoustically Driven Ferromagnetic Resonance (ADFMR) plots were generated for hybridized SAW/SW traveling in the (<b>A</b>) +z direction and (<b>B</b>) −z direction. Resonance absorption, highlighted in blue on the color scale, was observed at the ADFMR frequency in directions orthogonal to the growth field, where strong magneto-acoustic interaction took place. (<b>C</b>) Field sweeps at <span class="html-italic">ϕ</span> = 150° for forward (blue) and reverse (orange) SAW propagation. (<b>D</b>) Field sweeps at <span class="html-italic">ϕ</span> = 330° for forward (blue) and reverse (orange) propagation. The isolation was determined by the difference between forward and reverse sweeps under identical static field conditions. The nonreciprocal power isolation of 48.4 dB was observed. Reprinted with permission from Ref. [<a href="#B294-micromachines-15-01471" class="html-bibr">294</a>]. Copyright 2020 The American Association for the Advancement of Science.</p>
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<p>Wideband and giant nonreciprocity experimentally demonstrated in CoFeB/Ru/CoFeB RKKY stack. (<b>a</b>) Schematics of magnetoacoustic device. (<b>b</b>) SAW and SW dispersive relation near wide-band resonance region. (<b>c</b>) Wideband non-reciprocity from 2 to 7 GHz realized in CoFeB (20 nm)/Ru (0.46 nm)/CoFeB (20 nm) stack. (<b>d</b>) A 250 dB/mm giant non-reciprocity achieved in CoFeB (16 nm)/Ru (0.55 nm)/CoFeB (5 nm) stack. Image (<b>a</b>–<b>c</b>) is reprinted with permission from Ref. [<a href="#B304-micromachines-15-01471" class="html-bibr">304</a>]. Copyright 2024 American Chemical Society; Image (<b>d</b>) is reprinted with permission from Ref. [<a href="#B295-micromachines-15-01471" class="html-bibr">295</a>]. Copyright 2023 American Chemical Society.</p>
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<p>Magnetoelectric control of NV<sup>−</sup> center by CoFeB/PMN-PT BAW resonator. (<b>a</b>,<b>d</b>) Schematic illustration of the quantum spin defects (QSD)-magnon hybrid sample fabricated by dispersing nanodiamonds containing ensembles of NV<sup>−</sup> centers on a thin ferromagnetic film of CoFeB on a 300 μm thick PMN-PT ferroelectric substrate. (<b>b</b>,<b>e</b>) Maps of normalized <span class="html-italic">B</span> as a function of <span class="html-italic">ω</span>−<span class="html-italic">k</span> for both <span class="html-italic">V</span><sub>on</sub> and <span class="html-italic">V</span><sub>off</sub>. The black lines enveloping the colormap are the calculated magnon dispersion lines for bulk modes (<span class="html-italic">k</span>∥M) and surface modes (<span class="html-italic">k</span>⊥M). The dashed colored lines represent the NV<sup>−</sup> ESR lines <span class="html-italic">ω</span><sub>NV</sub>. (<b>c</b>) FMR frequency (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>m</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msubsup> </mrow> </semantics></math>) (data in black lines) as a function of applied voltage extracted from the experimental results for a fixed external magnetic field <span class="html-italic">H</span><sub>ext</sub> = 57 G along <span class="html-italic">x</span>-axis. The color map represents the calculated values of the magnetic noise spectral density <span class="html-italic">G</span><sub>m</sub>(<span class="html-italic">ω</span>, <span class="html-italic">V</span>) for an effective NV<sup>−</sup> height <span class="html-italic">d</span><sub>NV</sub> = 77 nm. The dashed colored lines represent the maximum spread of the NV<sup>−</sup> ESR lines <span class="html-italic">ω</span><sub>NV</sub>. The inset shows the detailed measurements of the magnetic anisotropy field as a function of applied voltage. (<b>f</b>) Measured relaxation rates Γ<sub>1</sub> as a function of applied voltage for a fixed <span class="html-italic">H</span><sub>ext</sub> = 57 G along the <span class="html-italic">x</span>-axis. The inset shows a schematic illustration of the magnetic anisotropy field for the two different voltages for a fixed <span class="html-italic">H</span><sub>ext</sub>. The dashed line represents the theoretical fit of relaxation rates Γ<sub>1.</sub> These figures are reproduced from Ref. [<a href="#B333-micromachines-15-01471" class="html-bibr">333</a>].</p>
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<p>Energy-efficient and local control of NV<sup>−</sup> centers by SAW-driven magnon resonance. (<b>a</b>) Plot of power absorption as a function of applied magnetic field for a 20 nm nickel ADFMR device at 1429 MHz. The x component of the field is taken to be parallel to the direction of SAW propagation, and the y component is in-plane and perpendicular to the direction of SAW propagation. The color bar indicates absorption in decibels per millimeter. (<b>b</b>) Line-cut along the angle of highest absorption (45°) showing a large field-dependent attenuation at 287, 861, and 229 MHz. The insets show the photograph of IDTs, magnetoelastic film, and clusters of nanodiamonds on the measured device. (<b>c</b>) Change in PL normalized to the DC level for NV<sup>−</sup> centers located off the ferromagnetic pad (red), and NV<sup>−</sup> centers on the pad with zero field (blue) and a high (35.8 mT) applied bias field (green) (<b>d</b>) NV<sup>−</sup> PL change in a 20 nm nickel sample as a function of longitudinal position from the edge of the ferromagnet closest to the excitation IDT at zero applied magnetic field. These figures are reproduced with permission from [<a href="#B334-micromachines-15-01471" class="html-bibr">334</a>]. Copyright 2018 The American Association for the Advancement of Science.</p>
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12 pages, 4586 KiB  
Technical Note
Advanced Dynamic Vibration Control Algorithms of Materials Terfenol-D Si3N4 and SUS304 Plates/Cylindrical Shells with Velocity Feedback Control Law
by Chih-Chiang Hong
Algorithms 2024, 17(12), 539; https://doi.org/10.3390/a17120539 - 25 Nov 2024
Viewed by 465
Abstract
A numerical, generalized differential quadrature (GDQ) method is presented on applied heat vibration for a thick-thickness magnetostrictive functionally graded material (FGM) plate coupled with a cylindrical shell. A nonlinear c1 term in the z axis direction of a third-order shear deformation theory [...] Read more.
A numerical, generalized differential quadrature (GDQ) method is presented on applied heat vibration for a thick-thickness magnetostrictive functionally graded material (FGM) plate coupled with a cylindrical shell. A nonlinear c1 term in the z axis direction of a third-order shear deformation theory (TSDT) displacement model is applied into an advanced shear factor and equation of motions, respectively. The equilibrium partial differential equation used for the thick-thickness magnetostrictive FGM layer plate coupled with the cylindrical shell under thermal and magnetostrictive loads can be implemented into the dynamic GDQ discrete equations. Parametric effects including nonlinear term coefficient of TSDT displacement field, advanced nonlinear varied shear coefficient, environment temperature, index of FGM power law and control gain on displacement, and stress of the thick magnetostrictive FGM plate coupled with cylindrical shell are studied. The vibrations of displacement and stress can be controlled by the control gain algorithms in velocity feedback control law. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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Graphical abstract

Graphical abstract
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<p>A magnetostrictive layer and two-material FGM plate coupled with a cylindrical shell by using velocity feedback control law.</p>
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<p>Advanced time responses of <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msup> <mi>h</mi> <mo>*</mo> </msup> </mrow> </semantics></math> = 5 for: (<b>a</b>) w(<span class="html-italic">a</span>/2,<span class="html-italic">b</span>/2)(mm) vs. <span class="html-italic">t</span>(s); (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>x</mi> </msub> </mrow> </semantics></math>(GPa) vs. <span class="html-italic">t</span>(s).</p>
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<p>Advanced w(<span class="html-italic">a</span>/2,<span class="html-italic">b</span>/2)(mm) vs. <span class="html-italic">T</span>(K) and <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>R</mi> <mi>n</mi> </msub> </mrow> </semantics></math> of <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msup> <mi>h</mi> <mo>*</mo> </msup> </mrow> </semantics></math> = 5 for: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">L</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>30</mn> </mrow> <mo>°</mo> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">L</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>60</mn> </mrow> <mo>°</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Advanced <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>x</mi> </msub> </mrow> </semantics></math>(GPa) versus <span class="html-italic">T</span>(K) and <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>R</mi> <mi>n</mi> </msub> </mrow> </semantics></math> of <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msup> <mi>h</mi> <mo>*</mo> </msup> </mrow> </semantics></math> = 5 for: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">L</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>30</mn> </mrow> <mo>°</mo> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">L</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>60</mn> </mrow> <mo>°</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Advanced transient responses of <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msup> <mi>h</mi> <mo>*</mo> </msup> </mrow> </semantics></math> = 5 for: (<b>a</b>) w(<span class="html-italic">a</span>/2,<span class="html-italic">b</span>/2)(mm) vs. <span class="html-italic">t</span>(s); (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>x</mi> </msub> </mrow> </semantics></math>(GPa) vs. <span class="html-italic">t</span>(s).</p>
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<p>Compared transient responses of <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>c</mi> </msub> <mi>c</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> = 0, 10<sup>9</sup> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mi mathvariant="normal">L</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>60</mn> </mrow> <mo>°</mo> </msup> </mrow> </semantics></math> for: (<b>a</b>) w(<span class="html-italic">a</span>/2,<span class="html-italic">b</span>/2)(mm) vs. <span class="html-italic">t</span>(s); (<b>b</b>)<math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>σ</mi> <mi>x</mi> </msub> </mrow> </semantics></math>(GPa) vs. <span class="html-italic">t</span>(s).</p>
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17 pages, 12577 KiB  
Article
Acoustic Tunnel Lining Void Detection: Modeling and Instrument System Development
by Luxin Tang, Jinbin Zeng, Chuixin Chen, Jian Huang, Shuxing Zhou, Li Wang, Defu Zhang, Weibin Wu and Ting Gao
Processes 2024, 12(12), 2651; https://doi.org/10.3390/pr12122651 - 25 Nov 2024
Viewed by 521
Abstract
The detachment of railway tunnel lining constitutes a grave danger to train operation safety and drastically curtails the tunnel’s service life. This study endeavors to efficiently detect the void defects in railway tunnel lining by creating a finite element model of tunnel lining [...] Read more.
The detachment of railway tunnel lining constitutes a grave danger to train operation safety and drastically curtails the tunnel’s service life. This study endeavors to efficiently detect the void defects in railway tunnel lining by creating a finite element model of tunnel lining structures. Utilizing this model, the study simulates the nonlinear acoustic wave propagation cloud maps for three representative tunnel lining structures: void-free, air void, and water void. This facilitates a thorough examination of the acoustic signal characteristics in the wavefield, time domain, and frequency domain. To satisfy the precision and efficiency demands of tunnel lining void detection, this study has devised and developed a portable acoustic detector that incorporates automatic analysis and processing capabilities and is furnished with a high-performance rare-earth magneto-strictive acoustic excitation device. This detection system can swiftly detect and assess typical void defects in tunnel lining. To further validate the effectiveness of this system, this study conducted lining defect detection in the Pingdao Railway Tunnel in the eastern Qinling Mountains. The test results show that the detection rate of this system for both air-filled and water-filled voids with a width of 1 m reached 100%, demonstrating its extremely high application value. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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<p>Tunnel concrete lining structure.</p>
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<p>Finite element geometric model diagram of tunnel concrete lining voiding structure.</p>
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<p>Mesh generation diagram of the finite element model for lining void structure.</p>
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<p>Scenes at the tunnel entrance.</p>
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<p>Scenes inside the tunnel.</p>
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<p>Schematic diagram of surveyed cross-section.</p>
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<p>Cloud diagrams of sound wave propagation at different times in non-void lining structures.</p>
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<p>Cloud diagrams of sound wave propagation at different times in air void lining structures.</p>
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<p>Cloud diagrams of Sound Wave Propagation at Different Times in Water-Filled Void Lining Structures.</p>
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<p>Waveform diagram of acoustic wave time-domain signal for tunnel lining void structure.</p>
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<p>Waveform diagram of acoustic wave time-domain signal for tunnel lining void structure.</p>
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<p>Time-domain reflected echo energy diagram of tunnel lining structure.</p>
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<p>Relationship diagram of time-domain reflected echo energy ratio versus void width <span class="html-italic">L</span>.</p>
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<p>Waveform diagram of acoustic wave frequency-domain signals for void-containing tunnel lining structures.</p>
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<p>Waveform diagram of acoustic wave frequency-domain signals for void-containing tunnel lining structures.</p>
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<p>Reflection echo energy ratio of frequency-domain signals for tunnel lining structures.</p>
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<p>Relationship diagram of frequency-domain reflected echo energy ratio versus void width <span class="html-italic">L</span>.</p>
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<p>Schematic diagram of acoustic wave detection system for void detection in lining structures.</p>
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<p>Principle and structural diagram of rare-earth giant MLT.</p>
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<p>Rare-earth giant MLT component.</p>
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<p>Test results for non-void area model.</p>
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<p>Test results for non-void area model.</p>
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<p>Test results for the model of water-filled void area.</p>
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13 pages, 3223 KiB  
Article
Coil-Only High-Frequency Lamb Wave Generation in Nickel Sheets
by Yini Song, Yihua Kang, Kai Wang, Yizhou Guo, Jun Tu and Bo Feng
Sensors 2024, 24(22), 7141; https://doi.org/10.3390/s24227141 - 6 Nov 2024
Viewed by 1450
Abstract
This study presents a novel, coil-only magnetostrictive ultrasonic detection method that operates effectively without permanent magnets, introducing a simpler alternative to conventional designs. The system configuration is streamlined, consisting of a single meander coil, an excitation source, and a nickel sheet, with both [...] Read more.
This study presents a novel, coil-only magnetostrictive ultrasonic detection method that operates effectively without permanent magnets, introducing a simpler alternative to conventional designs. The system configuration is streamlined, consisting of a single meander coil, an excitation source, and a nickel sheet, with both the bias magnetic field and ultrasonic excitation achieved by a composite excitation containing both DC and AC components. This design offers significant advantages, enabling high-frequency Lamb wave generation in nickel sheets for ultrasonic detection while reducing device complexity. Experimental validation demonstrated that an S0-mode Lamb wave at a frequency of 2.625 MHz could be effectively excited in a 0.2 mm nickel sheet using a double-layer meander coil. The experimentally measured wave velocity was 4.9946 m/s, with a deviation of only 0.4985% from the theoretical value, confirming the accuracy of the method. Additionally, this work provides a theoretical basis for future development of flexible MEMS-based magnetostrictive ultrasonic transducers, expanding the potential for miniaturized magnetostrictive patch transducers. Full article
(This article belongs to the Special Issue Advances and Applications of Magnetic Sensors)
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<p>Magnetostriction curve.</p>
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<p>Working principle and schematic diagram: (<b>a</b>) Single-coil magnetostrictive ultrasonic transducer; (<b>b</b>) DC component through the coil generates a static magnetic field (<span class="html-italic">H<sub>S</sub></span>), and the AC component produces a dynamic magnetic field (<span class="html-italic">H<sub>D</sub></span>).</p>
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<p>S-mode and A-mode Lamb wave propagation.</p>
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<p>Lamb wave frequency dispersion diagrams for: (<b>a</b>) 0.01 mm, (<b>b</b>) 0.2 mm and (<b>c</b>) 0.5 mm nickel sheets.</p>
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<p>Actual configuration of the experimental setup.</p>
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<p>FFT of an excitation signal from Sonemat pr-5000 obtained after connecting the coil.</p>
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<p>Double-layer meander coil with 2 mm wire spacing.</p>
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<p>The a−time domain signal of experimental group 1.</p>
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<p>FFT for the 0.2 mm nickel sheet: Results from experiment 1.</p>
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<p>Error bars for the 27 data sets.</p>
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23 pages, 2249 KiB  
Article
Improved EMAT Sensor Design for Enhanced Ultrasonic Signal Detection in Steel Wire Ropes
by Immanuel Rossteutscher, Oliver Blaschke, Florian Dötzer, Thorsten Uphues and Klaus Stefan Drese
Sensors 2024, 24(22), 7114; https://doi.org/10.3390/s24227114 - 5 Nov 2024
Viewed by 844
Abstract
This study is focused on optimizing electromagnetic acoustic transducer (EMAT) sensors for enhanced ultrasonic guided wave signal generation in steel cables using CAD and modern manufacturing to enable contactless ultrasonic signal transmission and reception. A lab test rig with advanced measurement and data [...] Read more.
This study is focused on optimizing electromagnetic acoustic transducer (EMAT) sensors for enhanced ultrasonic guided wave signal generation in steel cables using CAD and modern manufacturing to enable contactless ultrasonic signal transmission and reception. A lab test rig with advanced measurement and data processing was set up to test the sensors’ ability to detect cable damage, like wire breaks and abrasion, while also examining the effect of potential disruptors such as rope soiling. Machine learning algorithms were applied to improve the damage detection accuracy, leading to significant advancements in magnetostrictive measurement methods and providing a new standard for future development in this area. The use of the Vision Transformer Masked Autoencoder Architecture (ViTMAE) and generative pre-training has shown that reliable damage detection is possible despite the considerable signal fluctuations caused by rope movement. Full article
(This article belongs to the Special Issue Feature Papers in Physical Sensors 2024)
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Figure 1
<p>Schematic illustration of the generation of ultrasonic signals in steel cables by means of magnetostriction. The sound waves generated by the transmitter are influenced by defects in the steel cable. The sound waves are then detected by the receiver.</p>
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<p>Dispersion diagram of the phase velocity of different modes for a steel wire with similar dimensions as the experimental samples. Black curve: <math display="inline"><semantics> <mrow> <mi>F</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> fundamental mode. Red curve: <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> fundamental mode. Grey curves: higher-order <span class="html-italic">F</span> and <span class="html-italic">L</span> modes. Blue dashed line: excitation frequency of this study at 80 kHz.</p>
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<p>Example of a simulated configuration composed of the steel wire, surrounded by the pole shoes, permanent magnets, and iron yokes (<b>a</b>), the mesh used for the simulations (<b>b</b>), and the resulting magnetic flux density in Tesla (<b>c</b>).</p>
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<p>Setup with the steel wire encircled by pole shoes (<b>a</b>). Addition of permanent magnets directly on the pole shoes (<b>b</b>). Addition of iron yokes to help complete the magnetic circuit (<b>c</b>).</p>
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<p>Assembly of the EMAT sensor showing the housing that encloses the components, connecting rods that maintain alignment, and the coil form (<b>a</b>). Detailed view of the coil form, highlighting the three segments, each corresponding to half the wavelength (<math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>) of the ultrasonic waves (<b>b</b>).</p>
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<p>Photo of a fully assembled EMAT sensor for generating sound waves in steel cables. Neighbouring segments of the coil are wound in opposite directions to excite signals with a defined wavelength.</p>
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<p>Photo of the test rig designed for performing damage detection tests on steel cables.</p>
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<p>Impact of varying the number of magnet pairs and coil windings on the signal strength of ultrasonic signals for the receiver (<b>a</b>) and transmitter (<b>b</b>).</p>
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<p>Received signal consisting of the electromagnetic crosstalk of the excitation signal, the actual signal of interest, and a reflected signal from the end of the cable (<b>a</b>). Signal of interest (detailed view) detected by the receiving EMAT, which is used to analyse rope damage (<b>b</b>).</p>
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<p>Different measures for rope damage detection as boxplot analysis. (<b>Upper row</b>) centre frequency against either wire breaks or abrasion levels. (<b>Lower row</b>) time of flight against either wire breaks or abrasion levels.</p>
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<p>Principal components for intact and defective steel wire rope measurements. (<b>Left</b>) analysis of a blank steel rope with increasing number of wire breaks and abrasion levels. Principal component 1 relates to the progress of damage, while principal component 2 differentiates wire breaks from abrasion. (<b>Right</b>) analysis of a galvanised steel rope with increasing number of wire breaks, abrasion levels, and soiling effects.</p>
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<p>Confusion matrix of the classifier model for the bare steel wire rope (<b>left</b>) and for the galvanised steel wire rope (<b>right</b>).</p>
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<p>Predictions of the regressor models for the galvanised steel wire ropes on a test dataset. (<b>Left</b>) wire break predictions against real conditions. (<b>Right</b>) abrasion level predictions against real conditions.</p>
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<p>Comparison between the distributions of different features for a stationary cable (<b>a</b>) and a moving cable (<b>b</b>). While the features for the stationary cable are only slightly scattered, there is a significantly greater scatter of all features for the moving cable. As a result, it is no longer possible to distinguish clearly between defective and intact cable sections. The values are standardised in such a way that <math display="inline"><semantics> <mrow> <mn>100</mn> <mo>%</mo> </mrow> </semantics></math> corresponds to the mean value of the respective features of intact cable sections.</p>
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<p>Principle of generative pre-training with subsequent fine-tuning using a ViTMAE optimised for ultrasonic signals. The transformer consists of two main components. Firstly, the large encoder to obtain a robust feature space for a general understanding of ultrasonic signals. Secondly, a smaller decoder that is used to reconstruct the masked signal components. After completing the pre-training, only the encoder is used for the downstream task. Either the complete downstream model can be fine-tuned (full fine-tuning) or only the final classification layer (dense) with just 512 parameters (linear probing).</p>
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<p>Structure of the classifier neural network for the static case.</p>
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<p>Structure of the regressor neural network for the static case.</p>
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20 pages, 20556 KiB  
Article
A Contactless Low-Carbon Steel Magnetostrictive Torquemeter: Numerical Analysis and Experimental Validation
by Carmine Stefano Clemente, Claudia Simonelli, Nicolò Gori, Antonino Musolino, Rocco Rizzo, Marco Raugi, Alessandra Torri and Luca Sani
Sensors 2024, 24(21), 6949; https://doi.org/10.3390/s24216949 - 29 Oct 2024
Viewed by 661
Abstract
Torque measurement is a key task in several mechanical and structural engineering applications. Most commercial torquemeters require the shaft to be interrupted to place the sensors between the two portions of the shaft where a torque has to be measured. Contactless torquemeters based [...] Read more.
Torque measurement is a key task in several mechanical and structural engineering applications. Most commercial torquemeters require the shaft to be interrupted to place the sensors between the two portions of the shaft where a torque has to be measured. Contactless torquemeters based on the inverse magnetostrictive effect represent an effective alternative to conventional ones. Most known ferromagnetic materials have an inverse magnetostrictive behavior: applied stresses induce variations in their magnetic properties. This paper investigates the possibility of measuring torsional loads applied to a shaft made of ferromagnetic steel S235 through an inverse magnetostrictive torquemeter. It consists of an excitation coil that produces a time-varying electromagnetic field inside the shaft and an array of sensing coils suitably arranged around it, in which voltages are induced. First, the system is analyzed both in unloaded and loaded conditions by a Finite Element Method, investigating the influence of relative positions between the sensor and the shaft. Then, the numerical results are compared with the experimental measurements, confirming a linear characteristic of the sensor (sensitivity about 0.013 mV/Nm for the adopted experimental setup) and revealing the consistency of the model used. Since the system exploits the physical behavior of a large class of structural steel and does not require the introduction of special materials, this torquemeter may represent a reliable, economical, and easy-to-install device. Full article
(This article belongs to the Special Issue Magnetostrictive Transducers, Sensors, and Actuators)
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<p>Schematic view of the torque measurement system.</p>
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<p>Ampere-turn equivalent model of a sensor with an excitation coil and a single couple of sense coils.</p>
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<p>Meshed domain for the FE analysis: shaft portion and air box (<b>a</b>), and flux density distribution on the shaft surface (<b>b</b>).</p>
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<p>Complete sensor over a ferromagnetic shaft in air. The excitation and sensing coils layout over the under-testing shaft is visible. The pickup coils 1 and 4, 2 and 5, and 3 and 6 are electrically connected in series.</p>
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<p>Amplitudes of the induced voltages as functions of the gap.</p>
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<p>Amplitudes of the induced voltages with respect to the pitch angle.</p>
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<p>Amplitudes of the induced voltages with respect to the displacement along the x-axis.</p>
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<p>Amplitudes of the induced voltages with respect to the yaw angle.</p>
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<p>FE model of the analyzed geometry.</p>
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<p>Amplitude of the magnetic flux density in the 3D FE model at 0 Nm (<b>a</b>), 600 Nm (<b>b</b>), and 1200 Nm (<b>c</b>). Values are expressed in milliTesla.</p>
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<p>FE computed sensing coils peak voltages versus applied pure torque.</p>
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<p>FE computed sensing coils peak voltage difference (with respect to torque = 0 Nm) versus applied pure torque.</p>
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<p>Sample shaft used to test the proposed system coupled to a 2 m long bar and a test rig.</p>
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<p>Experimental setup used to produce the static mechanical excitation.</p>
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<p>Sample shaft under test with mounted probehead (<b>a</b>) and 3D printed probehead support (<b>b</b>).</p>
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<p>Peak voltages on the sensing coils as a function of applied pure torque. Experimental results.</p>
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<p>Sensing coils peak voltage difference (with respect to null torque) versus applied pure torque. Experimental results.</p>
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<p>Sensing coils peak voltage difference (with respect to null load) versus applied torque in case of non-pure torque test. Experimental results.</p>
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<p>Sensing coils peak voltage versus applied torque: loading and unloading cycle. Experimental results.</p>
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<p>Sensing coils peak voltages versus yaw angles, in unloaded shaft conditions. Experimental results.</p>
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16 pages, 21094 KiB  
Article
Development of a Meander-Coil-Type Dual Magnetic Group Circumferential Magnetostrictive Guided Wave Transducer for Detecting Small Defects Hidden behind Support Structures
by Jinjie Zhou, Hang Zhang, Yuepeng Chen and Jitang Zhang
Micromachines 2024, 15(10), 1261; https://doi.org/10.3390/mi15101261 - 15 Oct 2024
Viewed by 827
Abstract
In order to solve the problem that small defects hidden behind pipeline support parts are difficult to detect effectively in small spaces, such as offshore oil platforms, a meander-coil-type dual magnetic group circumferential magnetostrictive guided wave transducer is developed in this paper. The [...] Read more.
In order to solve the problem that small defects hidden behind pipeline support parts are difficult to detect effectively in small spaces, such as offshore oil platforms, a meander-coil-type dual magnetic group circumferential magnetostrictive guided wave transducer is developed in this paper. The transducer, which consists of a coil, two sets of permanent magnets, and a magnetostrictive patch, can excite a high-frequency circumferential shear horizontal (CSH) guided wave. The energy conversion efficiency of the MPT is optimized through magnetic field simulation and experiment, and the amplitude of the defect signal is enhanced 1.9 times. The experimental results show that the MPT developed in this paper can effectively excite and receive CSH2 mode guided waves with a center frequency of 1.6 MHz. Compared with the traditional PPM EMAT transducer, the excitation energy of the transducer is significantly enhanced, and the defects of the 2 mm round hole at the back of the support can be effectively detected. Full article
(This article belongs to the Special Issue Acoustic Transducers and Their Applications, 2nd Edition)
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<p>Specific structure of the transducer.</p>
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<p>The theoretical dispersion curve of the SH wave: (<b>a</b>) phase velocity dispersion curve; (<b>b</b>) group velocity dispersion curve.</p>
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<p>Transducer working principle diagram.</p>
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<p>Electromagnetic ultrasonic high-order SH wave mode experimental system and schematic diagram of experimental operation.</p>
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<p>Magnetic field simulation in magnetostrictive patches. (<b>a</b>) Schematic diagram of dynamic magnetic field changes. (<b>b</b>) Dynamic magnetic field transient change curve. (<b>c</b>) Maximum magnetic field curve.</p>
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<p>Simulation results of the influence of different rows of magnets on a static biased magnetic field in a magnetostrictive patch.</p>
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<p>(<b>a</b>)Transducer and pipeline defect location. (<b>b</b>) Direct wave signal.</p>
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<p>Comparison of defect detection signals of transducers with different rows of magnets.</p>
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<p>Simulation results of the static biased magnetic field of the magnetostrictive patch. (<b>a</b>) The effect of adjusting the magnet size on the static magnetic field. (<b>b</b>) The effect of adjusting the lifting distance on the static magnetic field.</p>
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<p>The received signal: (<b>a</b>,<b>c</b>,<b>e</b>) are signals received by the transducer when the 3 mm, 7 mm, and 10 mm magnets are not lifted. (<b>b</b>) The signal received by the transducer at the maximum lift of the 3 mm magnet; (<b>d</b>,<b>f</b>) are the best signals received by transducers with 7 mm and 10 mm magnets. (<b>g</b>) Defect detection signals received by transducers with different magnet sizes and lift distances.</p>
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<p>The received signal. (<b>a</b>) The signal received by the transducer when the magnetostrictive material is FeCoV. (<b>b</b>) The signal received by the transducer when the magnetostrictive material is Ni.</p>
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<p>Schematic diagram of transducer layout and pipeline defect location.</p>
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<p>The received signal. (<b>a</b>) Detection signals for defects of different sizes and types. (<b>b</b>) Defect echo signals.</p>
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<p>The received signal. (<b>a</b>) Received signal from the PPM EMAT. (<b>b</b>) Received signal of the MPT.</p>
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14 pages, 4685 KiB  
Article
Magnetostrictive Behavior of Severe Plastically Deformed Nanocrystalline Fe-Cu Materials
by Alexander Paulischin, Stefan Wurster, Heinz Krenn and Andrea Bachmaier
Metals 2024, 14(10), 1157; https://doi.org/10.3390/met14101157 - 11 Oct 2024
Viewed by 687
Abstract
Reducing the saturation magnetostriction is an effective way to improve the performance of soft magnetic materials and reduce core losses in present and future applications. The magnetostrictive properties of binary Fe-based alloys are investigated for a broad variety of alloying elements. Although several [...] Read more.
Reducing the saturation magnetostriction is an effective way to improve the performance of soft magnetic materials and reduce core losses in present and future applications. The magnetostrictive properties of binary Fe-based alloys are investigated for a broad variety of alloying elements. Although several studies on the influence of Cu-alloying on the magnetic properties of Fe are reported, few studies have focused on the effect on its magnetostrictive behavior. High pressure torsion deformation is a promising fabrication route to produce metastable, single-phase Fe-Cu alloys. In this study, the influence of Cu-content and the chosen deformation parameters on the microstructural and phase evolution in the Fe-Cu system is investigated by scanning electron microscopy and synchrotron X-ray diffraction. Magnetic properties and magnetostrictive behavior are measured as well. While a reduction in the saturation magnetostriction λs is present for all Cu-contents, two trends are noticeable. λs decreases linearly with decreasing Fe-content in Fe-Cu nanocomposites, which is accompanied by an increasing coercivity. In contrast, both the saturation magnetostriction as well as the coercivity strongly decrease in metastable, single-phase Fe-Cu alloys after HPT-deformation. Full article
(This article belongs to the Special Issue Advances in Magnetic Alloys)
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<p>(<b>a</b>) A schematic illustration of the sample preparation for the two-step deformation process with the first deformation step conducted on the big HPT-tool. From the obtained big sample, a strip (green) was cut out, from which the new sample (blue disc) for the second HPT-deformation step was fabricated. (<b>b</b>) A schematic illustration of a bisected small HPT disc with the areas, where measurements were conducted, marked as colored surfaces. The color code of the captions refers to the colored surfaces. The inset shows a sample after HPT-deformation. The black bar is in the size of 10 mm. The orthogonal reference system “axial–radial–tangential” refers to (<b>a</b>,<b>b</b>). The radial positions are highlighted.</p>
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<p>BSE images of (<b>a</b>) Fe after 20 rotations as well as (<b>b</b>) Fe<sub>95</sub>Cu<sub>5</sub> No. 1, (<b>c</b>) Fe<sub>95</sub>Cu<sub>5</sub> No. 2, (<b>d</b>) Fe<sub>85</sub>Cu<sub>15</sub> No. 1 *, (<b>e</b>) Fe<sub>85</sub>Cu<sub>15</sub> No. 2 and (<b>f</b>) Fe<sub>70</sub>Cu<sub>30</sub> after the second deformation step at a radial position of 2 mm. The Cu-content in at.% determined by EDS is given in the blue boxes. The mean hardness values are given in the green boxes. The scalebar in (<b>a</b>) refers to all microstructures in <a href="#metals-14-01157-f002" class="html-fig">Figure 2</a>. The coordinate system in (<b>a</b>) refers to all subsequent BSE images. All obtained hardness values have been previously published in ref. [<a href="#B25-metals-14-01157" class="html-bibr">25</a>].</p>
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<p>(<b>a</b>) BSE images of Fe<sub>95</sub>Cu<sub>5</sub> No. 1 after the second deformation step at a radial position of 0 mm, 1 mm, 2 mm and 3 mm. (<b>b</b>) The corresponding diffraction patterns. The positions and intensities of the reference patterns are indicated as colored bars. Measurements were carried out at DESY PETRA III at beamline P07B.</p>
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<p>(<b>a</b>) BSE images of Fe<sub>85</sub>Cu<sub>15</sub> No. 1 * after the second deformation step at a radial position of 0 mm, 1 mm, 2 mm and 3 mm. (<b>b</b>) The corresponding diffraction patterns. The positions and intensities of the reference patterns are indicated as colored bars. Measurements were carried out at DESY PETRA III at beamline P21.2.</p>
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<p>(<b>a</b>) Hysteresis loops determined by SQUID magnetometry of the investigated Fe-Cu system after the second HPT-deformation step. The inset gives a detailed view of the intercepts of the hysteresis loops with the abscissa. (<b>b</b>) Evolution of coercivity <span class="html-italic">H<sub>c</sub></span>, remanence <span class="html-italic">M<sub>r</sub></span> and saturation magnetization <span class="html-italic">M<sub>s</sub></span> in dependence on the Cu-concentration.</p>
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<p>Saturation magnetostriction <span class="html-italic">λ<sub>s</sub></span> and its dependence on the determined Cu-concentration. The blue, red and magenta triangles are reference values of <span class="html-italic">λ<sub>s</sub></span> for polycrystalline Fe [<a href="#B2-metals-14-01157" class="html-bibr">2</a>,<a href="#B24-metals-14-01157" class="html-bibr">24</a>,<a href="#B27-metals-14-01157" class="html-bibr">27</a>]. The dashed lines, which enclose the gray area, are a linear approximation of <span class="html-italic">λ<sub>s</sub></span> in dependence on Cu-content, following a simple rule of mixture. All values of <span class="html-italic">λ<sub>s</sub></span> have been previously published in ref. [<a href="#B25-metals-14-01157" class="html-bibr">25</a>].</p>
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15 pages, 3024 KiB  
Article
Combining Magnetostriction with Variable Reluctance for Energy Harvesting at Low Frequency Vibrations
by Johan Bjurström, Cristina Rusu and Christer Johansson
Appl. Sci. 2024, 14(19), 9070; https://doi.org/10.3390/app14199070 - 8 Oct 2024
Viewed by 934
Abstract
In this paper, we explore the benefits of using a magnetostrictive component in a variable reluctance energy harvester. The intrinsic magnetic field bias and the possibility to utilize magnetic force to achieve pre-stress leads to a synergetic combination between this type of energy [...] Read more.
In this paper, we explore the benefits of using a magnetostrictive component in a variable reluctance energy harvester. The intrinsic magnetic field bias and the possibility to utilize magnetic force to achieve pre-stress leads to a synergetic combination between this type of energy harvester and magnetostriction. The proposed energy harvester system, to evaluate the concept, consists of a magnetostrictive cantilever beam with a cubic magnet as proof mass. Galfenol, Fe81.6Ga18.4, is used to implement magnetostriction. Variable reluctance is achieved by fixing the beam parallel to an iron core, with some margin to create an air gap between the tip magnet and core. The mechanical forces of the beam and the magnetic forces lead to a displaced equilibrium position of the beam and thus a pre-stress. Two configurations of the energy harvester were evaluated and compared. The initial configuration uses a simple beam of aluminum substrate and a layer of galfenol with an additional magnet fixing the beam to the core. The modified design reduces the magnetic field bias in the galfenol by replacing approximately half of the length of galfenol with aluminum and adds a layer of soft magnetic material above the galfenol to further reduce the magnetic field bias. The initial system was found to magnetically saturate the galfenol at equilibrium. This provided the opportunity to compare two equivalent systems, with and without a significant magnetostrictive effect on the output voltage. The resonance frequency tuning capability, from modifying the initial distance of the air gap, is shown to be maintained for the modified configuration (140 Hz/mm), while achieving RMS open-circuit coil voltages larger by a factor of two (2.4 V compared to 1.1 V). For a theoretically optimal load, the RMS power was simulated to be 5.1 mW. Given the size of the energy harvester (18.5 cm3) and the excitation acceleration (0.5 g), this results in a performance metric of 1.1 mW/cm3g2. Full article
(This article belongs to the Topic Advanced Energy Harvesting Technology)
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Figure 1

Figure 1
<p>Cross-section of the proposed energy harvester design, with iron core (gray), neodymium magnets (blue/red), aluminum substrate (green) and galfenol magnetostrictive layer (purple). Iron core components are numbered, 1 to 6, and are referred to in the main text.</p>
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<p>Hypothetical linear and square-dependent forces representing an ideal version of the system described in this work. Dashed lines correspond to the mechanical spring force at three different initial air gaps. The solid line corresponds to the magnetic force. Dots represent stable equilibria and arrows represent unstable equilibria.</p>
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<p>(<b>a</b>) The 3D CAD of COMSOL model geometry, with iron (dark blue), neodymium (light blue), aluminum (dark red), galfenol (green) and polyamide (orange). (<b>b</b>) Prototype for lab measurements. The energy harvester is here mounted on top of the shaker.</p>
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<p>RMS of the open-circuit coil voltage. Curves from right to left result from using an increasingly thicker spacer, i.e., increasing β. (<b>a</b>) Simulated values. Circles and crosses are data points. Solid lines correspond to using λ<sub>S</sub> = 200 and dashed lines for λ<sub>S</sub> = 0. (<b>b</b>) Measured on prototype. Dots are data points. Lines are for visual aid.</p>
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<p>Simulation results, for the original design, in the vicinity of the magnetostrictive component. (<b>a</b>) von Mises stress distributions. (<b>b</b>) Magnetization, λ<sub>S</sub> = 200. (<b>c</b>) Magnetization, λ<sub>S</sub> = 0.</p>
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<p>Revised design. Compared to the original design, one magnet is removed, while the neodymium magnet (blue/red) acting as proof mass remains. The beam composition consists of cobalt steel Vacoflux 50 (light blue), galfenol (purple) and aluminum (green). The iron core components (gray) are identical to the original design.</p>
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<p>Simulation results, for the modified design, in the vicinity of magnetostrictive component. (<b>a</b>) von Mises stress distributions. (<b>b</b>) Magnetization, λ<sub>S</sub> = 200. (<b>c</b>) Magnetization, λ<sub>S</sub> = 0.</p>
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<p>RMS of the simulated open-circuit coil voltage for the modified design. Curves from right to left result from increasing values of β. Circles, dots and crosses are data points. Lines are added as visual aid. Solid lines correspond to using λ<sub>S</sub> = 200 and dashed lines for λ<sub>S</sub> = 0.</p>
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<p>Simulated O/C RMS coil voltage at resonance and at the end of the time series. (<b>a</b>) β from 4.5 mm to 4.7 mm. (<b>b</b>) β from 4.8 mm to 4.95 mm.</p>
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12 pages, 4580 KiB  
Article
A Polyimide Composite-Based Electromagnetic Cantilever Structure for Smart Grid Current Sensing
by Zeynel Guler and Nathan Jackson
Micromachines 2024, 15(10), 1189; https://doi.org/10.3390/mi15101189 - 26 Sep 2024
Viewed by 3683
Abstract
Polyimides (PIs) have been extensively used in thin film and micro-electromechanical system (MEMS) processes based on their excellent thermal and mechanical stability and high glass transition temperature. This research explores the development of a novel multilayer and multifunctional polymer composite electro-piezomagnetic device that [...] Read more.
Polyimides (PIs) have been extensively used in thin film and micro-electromechanical system (MEMS) processes based on their excellent thermal and mechanical stability and high glass transition temperature. This research explores the development of a novel multilayer and multifunctional polymer composite electro-piezomagnetic device that can function as an energy harvester or sensor for current-carrying wires or magnetic field sensing. The devices consist of four layers of composite materials with a polyimide matrix. The composites have various nanoparticles to alter the functionality of each layer. Nanoparticles of Ag were used to increase the electrical conductivity of polyimide and act as electrodes; lead zirconate titanate was used to make the piezoelectric composite layer; and either neodymium iron boron (NdFeB) or Terfenol-D was used to make the magnetic and magnetostrictive composite layer, which was used as the proof mass. A novel all-polymer multifunctional polyimide composite cantilever was developed to operate at low frequencies. This paper compares the performance of the different magnetic masses, shapes, and concentrations, as well as the development of an all-magnetostrictive device to detect voltage or current changes when coupled to the magnetic field from a current-carrying wire. The PI/PZT cantilever with the PI/NdFeB proof mass demonstrated higher voltage output compared to the PI/Terfenol-D proof mass device. However, the magnetostrictive composite film could be operated without a piezoelectric film based on the Villari effect, which consisted of a single PI-Terfenol-D film. The paper illustrates the potential to develop an all-polymer composite MEMS device capable of acting as a magnetic field or current sensor. Full article
(This article belongs to the Section E:Engineering and Technology)
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Figure 1

Figure 1
<p>(<b>a</b>) Schematic diagram illustrating the actuation mechanism, (<b>b</b>) schematic of the four-layered all-polyimide composite cantilever structure, and (<b>c</b>) a single PI-Terfenol-D magnetostrictive film with integrated coils where τ is the torque and N and S are the poles of the magnet.</p>
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<p>Schematic diagram illustrating manufacturing of PI composite film.</p>
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<p>Experimental testing: (<b>a</b>) single conducting wire and (<b>b</b>) Helmholtz coil setup.</p>
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<p>Magnetic field strength graph between Helmholtz coils (yellow circles) based on gaussmeter measurements.</p>
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<p>Voltage output of the 40 wt.% multilayered sensor using 1 A in Helmholtz coil: (<b>a</b>) NdFeB-PI magnetic proof mass and (<b>b</b>) Terfenol-D–PI magnetostrictive proof mass.</p>
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<p>Experimental setup with various shaped proof masses: (<b>a</b>) long rectangle, (<b>b</b>) triangle, and (<b>c</b>) short rectangle, coupled to a single Cu wire to determine spatial resolution.</p>
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<p>Spatial resolution comparison of (<b>a</b>) thin film devices versus (<b>b</b>) bulk devices [<a href="#B20-micromachines-15-01189" class="html-bibr">20</a>].</p>
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<p>Voltage output of piezoelectric composite with magnetic proof mass (<b>a</b>) as a function of applied magnetic field and (<b>b</b>) as a function of NdFeB composition.</p>
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<p>(<b>a</b>) Triangular-shaped magnetostrictive films with different Terfenol-D concentrations and spin coating speeds (1k, 3k, and 6k), (<b>b</b>) the experimental setup to measure tip displacement under various magnetic fields.</p>
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<p>Tip deflection of triangular-shaped Terfenol-D–PI films with (<b>a</b>) varying thickness and composition and (<b>b</b>) 20% Terfenol with 23 μm thickness with varying applied current.</p>
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<p>Current output of Terfenol-D–PI composite film with a magnetic field of 0.012 T.</p>
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17 pages, 2821 KiB  
Article
On the Piezomagnetism of Magnetoactive Elastomeric Cylinders in Uniform Magnetic Fields: Height Modulation in the Vicinity of an Operating Point by Time-Harmonic Fields
by Gašper Glavan, Inna A. Belyaeva and Mikhail Shamonin
Polymers 2024, 16(19), 2706; https://doi.org/10.3390/polym16192706 - 25 Sep 2024
Viewed by 5780
Abstract
Soft magnetoactive elastomers (MAEs) are currently considered to be promising materials for actuators in soft robotics. Magnetically controlled actuators often operate in the vicinity of a bias point. Their dynamic properties can be characterized by the piezomagnetic strain coefficient, which is a ratio [...] Read more.
Soft magnetoactive elastomers (MAEs) are currently considered to be promising materials for actuators in soft robotics. Magnetically controlled actuators often operate in the vicinity of a bias point. Their dynamic properties can be characterized by the piezomagnetic strain coefficient, which is a ratio of the time-harmonic strain amplitude to the corresponding magnetic field strength. Herein, the dynamic strain response of a family of MAE cylinders to the time-harmonic (frequency of 0.1–2.5 Hz) magnetic fields of varying amplitude (12.5 kA/m–62.5 kA/m), superimposed on different bias magnetic fields (25–127 kA/m), is systematically investigated for the first time. Strain measurements are based on optical imaging with sub-pixel resolution. It is found that the dynamic strain response of MAEs is considerably different from that in conventional magnetostrictive polymer composites (MPCs), and it cannot be described by the effective piezomagnetic constant from the quasi-static measurements. The obtained maximum values of the piezomagnetic strain coefficient (∼102 nm/A) are one to two orders of magnitude higher than in conventional MPCs, but there is a significant phase lag (35–60°) in the magnetostrictive response with respect to an alternating magnetic field. The experimental dependencies of the characteristics of the alternating strain on the amplitude of the alternating field, bias field, oscillation frequency, and aspect ratio of cylinders are given for several representative examples. It is hypothesized that the main cause of observed peculiarities is the non-linear viscoelasticity of these composite materials. Full article
(This article belongs to the Special Issue Advances in Functional Rubber and Elastomer Composites II)
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Graphical abstract

Graphical abstract
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<p>Schematic diagram of the dynamic behavior of a conventional MS actuator driven by a time-harmonic magnetic field in the vicinity of a bias point (<math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>). The red dash-dotted line denotes the tangent of the curve <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo> </mrow> </semantics></math> at point <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) Schematic diagram of the experimental setup. (<b>b</b>) Images of an isotropic MAE cylinder with an iron content 75 wt% and an aspect ratio <math display="inline"><semantics> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> </semantics></math> of <math display="inline"><semantics> <mrow> <mn>1.2</mn> </mrow> </semantics></math> in a zero magnetic field (<b>left</b> side) and in a maximum magnetic field (<b>right</b> side).</p>
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<p>Macroscopic deformation of an isotropic MAE cylinder with 75 wt% of Fe and an aspect ratio <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math>. Here and below, a line connecting experimental points serves as a guide to the eye. (<b>a</b>) Magnetostrictive hysteresis loops with additional minor loops due to superimposed oscillations of a magnetic field at different operation points. (<b>b</b>) Example of the transient response of magnetostrictive strain in a magnetic field (<a href="#FD1-polymers-16-02706" class="html-disp-formula">1</a>). The measured values are shown in blue, and the fitted sinusoidal function is shown as a red curve. The bias field of 77 kA/m was set at the time point of <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>60</mn> </mrow> </semantics></math> s. (<b>c</b>) Longitudinal strain <math display="inline"><semantics> <mi>λ</mi> </semantics></math> versus the momentary value of magnetic field for the case (<b>b</b>). The red ellipse demonstrates the result from the fitted function (<a href="#FD2-polymers-16-02706" class="html-disp-formula">2</a>). (<b>d</b>) Comparison of magnetostrictive response when magnetic field oscillations started with opposite phases (<math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> had the same magnitude, but it was either positive or negative). In (<b>b</b>–<b>d</b>), magnetic field oscillations had a frequency <span class="html-italic">f</span> of 1.0 Hz, an oscillation amplitude <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> was 25 kA/m, and a bias magnetic field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> was 77 kA/m.</p>
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<p>Dependencies of different characteristics of the alternating strain <math display="inline"><semantics> <msub> <mi>λ</mi> <mo>∼</mo> </msub> </semantics></math> with a frequency <span class="html-italic">f</span> = 1.0 Hz on the magnitude of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> for isotropic MAE cylinders with three different weight fractions of Fe (70, 75, 80 wt%) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> in ascending (“up”) or descending (“down”) bias field <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>77</mn> </mrow> </semantics></math> kA/m of a quasi-static magnetostrictive hysteresis loop. In all sub-figures, a specific line color refers to the same value of iron content and the same part of hysteresis loop (ascending/descending). (<b>a</b>) The amplitude of harmonic strain oscillation <math display="inline"><semantics> <msub> <mi>λ</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. (<b>b</b>) Piezomagnetic coefficient <math display="inline"><semantics> <msub> <mi>d</mi> <mn>33</mn> </msub> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. (<b>c</b>) Phase lag <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. (<b>d</b>) Lissajous figures for different values of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. Continuous lines refer to <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>12.5</mn> </mrow> </semantics></math> kA/m, dashed lines refer to <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>37.5</mn> </mrow> </semantics></math> kA/m, and dash-dotted lines refer to <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>62.5</mn> </mrow> </semantics></math> kA/m.</p>
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<p>Dependencies of different characteristics of the alternating strain <math display="inline"><semantics> <msub> <mi>λ</mi> <mo>∼</mo> </msub> </semantics></math> with a frequency <span class="html-italic">f</span> = 1.0 Hz on the magnitude of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> for isotropic MAE cylinders with three different weight fractions of Fe (70, 75, 80 wt%), and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> in the ascending (“up”) or descending (“down”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> of a quasi-static magnetostrictive hysteresis loop. The value of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> is fixed at 25 kA/m. In all sub-figures, a specific line color refers to the same value of iron content and the same part of hysteresis loop (ascending/descending). (<b>a</b>) <math display="inline"><semantics> <msub> <mi>d</mi> <mn>33</mn> </msub> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. Dashed black line designates the position of the maximums of <span class="html-italic">d</span> for the descending part of the quasi-static hysteresis curves. (<b>b</b>) <span class="html-italic">d</span> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>, calculated as a finite central difference from experimental results of [<a href="#B41-polymers-16-02706" class="html-bibr">41</a>]. Black arrows designate the direction of field change. (<b>c</b>) Phase delay <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. (<b>d</b>) Lissajous figures for different values of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. Continuous lines refer to <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>52</mn> </mrow> </semantics></math> kA/m, dashed lines refer to <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>102</mn> </mrow> </semantics></math> kA/m, and dash-dotted lines refer to <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>25</mn> </mrow> </semantics></math> kA/m.</p>
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<p>Dependencies of different characteristics of the alternating strain <math display="inline"><semantics> <msub> <mi>λ</mi> <mo>∼</mo> </msub> </semantics></math> with a frequency <span class="html-italic">f</span> = 1.0 Hz on the magnitude of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> for anisotropic MAE cylinders with three different weight fractions of Fe (70, 75, 80 wt%), and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> in ascending (“up”) or descending (“down”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> of a quasi-static magnetostrictive hysteresis loop. The value of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> is fixed at 25 kA/m. In all sub-figures, a specific line color refers to the same value of iron content and the same part of hysteresis loop (ascending/descending). (<b>a</b>) <math display="inline"><semantics> <msub> <mi>d</mi> <mn>33</mn> </msub> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. (<b>b</b>) Phase delay <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. (<b>c</b>) Lissajous figures for different values of ascending (“up”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>. (<b>d</b>) Lissajous figures for different values of descending (“down”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Dependencies of different characteristics of the alternating strain <math display="inline"><semantics> <msub> <mi>λ</mi> <mo>∼</mo> </msub> </semantics></math> on the oscillation frequency <span class="html-italic">f</span> for isotropic MAE cylinders with three different weight fractions of Fe (70, 75, 80 wt%) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> in ascending (“up”) or descending (“down”) bias field of a quasi-static magnetostrictive hysteresis loop. The value of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> is fixed at 25 kA/m. The value of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> is fixed at 77 kA/m. In all sub-figures, a specific line color refers to the same value of iron content and the same part of the hysteresis loop (ascending/descending). (<b>a</b>) <math display="inline"><semantics> <msub> <mi>d</mi> <mn>33</mn> </msub> </semantics></math> versus <span class="html-italic">f</span>. (<b>b</b>) Phase delay <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> versus <span class="html-italic">f</span>. (<b>c</b>) Lissajous figures for different values of frequency <span class="html-italic">f</span> in an ascending (“up”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> of 77 kA/m. (<b>d</b>) Lissajous figures for different values of frequency <span class="html-italic">f</span> in a descending (“down”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> of 77 kA/m.</p>
Full article ">Figure 8
<p>Dependencies of different characteristics of the alternating strain <math display="inline"><semantics> <msub> <mi>λ</mi> <mo>∼</mo> </msub> </semantics></math> on the aspect ratio <math display="inline"><semantics> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> </semantics></math> for isotropic MAE cylinders with 75 wt% of Fe in ascending (“up”) or descending (“down”) bias field of a quasi-static magnetostrictive hysteresis loop. The value of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> </semantics></math> is fixed at 25 kA/m. The value of <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> is fixed at 77 kA/m. The frequency <span class="html-italic">f</span> is fixed at 1.0 Hz. In all sub-figures, a specific line color refers to the same part of the hysteresis loop (ascending/descending). (<b>a</b>) <math display="inline"><semantics> <msub> <mi>d</mi> <mn>33</mn> </msub> </semantics></math> versus <math display="inline"><semantics> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> </semantics></math>. (<b>b</b>) Phase delay <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> versus aspect ratio <math display="inline"><semantics> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> </semantics></math>. (<b>c</b>) Lissajous figures for different aspect ratios <math display="inline"><semantics> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> </semantics></math> in an ascending (“up”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> of 77 kA/m. (<b>d</b>) Lissajous figures for different aspect ratios <math display="inline"><semantics> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> </semantics></math> in a descending (“down”) bias field <math display="inline"><semantics> <msub> <mi>H</mi> <mrow> <mi>D</mi> <mi>C</mi> </mrow> </msub> </semantics></math> of 77 kA/m. Dash-dotted lines correspond to <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, continuous lines correspond to <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, and dashed lines correspond to <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Γ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math>.</p>
Full article ">Figure A1
<p>Time dependencies of the longitudinal strain (blue curve) for harmonic magnetic field modulations (orange curve) when the DC magnetic field is increasing (<b>a</b>) and when it is decreasing (<b>b</b>). Parameters of the sample and measurement conditions are given within the figures.</p>
Full article ">Figure A2
<p>Magnetostrictive response to oscillating magnetic field when the bias magnetic field is increasing (<b>a</b>) and when the bias field is decreasing (<b>b</b>). Blue dots and lines refer to the positive value of <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>25</mn> </mrow> </semantics></math> kA/m, and orange dots and lines refer to the negative value of <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mn>25</mn> </mrow> </semantics></math> kA/m. Parameters of the sample and measurement conditions are given within the figures.</p>
Full article ">
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