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28 pages, 14370 KiB  
Article
Experimental Study on Mechanical Performance of Single-Side Bonded Carbon Fibre-Reinforced Plywood for Wood-Based Structures
by Krzysztof Szwajka, Joanna Zielińska-Szwajka, Tomasz Trzepieciński and Marek Szewczyk
Materials 2025, 18(1), 207; https://doi.org/10.3390/ma18010207 - 6 Jan 2025
Abstract
In addition to the traditional uses of plywood, such as furniture and construction, it is also widely used in areas that benefit from its special combination of strength and lightness, particularly as a construction material for the production of finishing elements of campervans [...] Read more.
In addition to the traditional uses of plywood, such as furniture and construction, it is also widely used in areas that benefit from its special combination of strength and lightness, particularly as a construction material for the production of finishing elements of campervans and yachts. In light of the current need to reduce emissions of climate-damaging gases such as CO2, the use of lightweight construction materials is very important. In recent years, hybrid structures made of carbon fibre-reinforced plastics (CFRPs) and metals have attracted much attention in many industries. In contrast to hybrid metal/carbon fibre composites, research relating to laminates consisting of CFRPs and wood-based materials shows less interest. This article analyses the hybrid laminate resulting from bonding a CFRP panel to plywood in terms of strength and performance using a three-point bending test, a static tensile test and a dynamic analysis. Knowledge of the dynamic characteristics of carbon fibre-reinforced plywood allows for the adoption of such cutting parameters that will help prevent the occurrence of self-excited vibrations in the cutting process. Therefore, in this work, it was decided to determine the effect of using CFRP laminate on both the static and dynamic stiffness of the structure. Most studies in this field concern improving the strength of the structure without analysing the dynamic properties. This article proposes a simple and user-friendly methodology for determining the damping of a sandwich-type system. The results of strength tests were used to determine the modulus of elasticity, modulus of rupture, the position of the neutral axis and the frequency domain characteristics of the laminate obtained. The results show that the use of a CFRP-reinforced plywood panel not only improves the visual aspect but also improves the strength properties of such a hybrid material. In the case of a CFRP-reinforced plywood panel, the value of tensile stresses decreased by sixteen-fold (from 1.95 N/mm2 to 0.12 N/mm2), and the value of compressive stresses decreased by more than seven-fold (from 1.95 N/mm2 to 0.27 N/mm2) compared to unreinforced plywood. Based on the stress occurring at the tensile and compressive sides of the CFRP-reinforced plywood sample surface during a cantilever bending text, it was found that the value of modulus of rupture decreased by three-fold and the value of the modulus of elasticity decreased by more than five-fold compared to the unreinforced plywood sample. A dynamic analysis allowed us to determine that the frequency of natural vibrations of the CFRP-reinforced plywood panel increased by about 33% (from 30 Hz to 40 Hz) compared to the beam made only of plywood. Full article
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Figure 1
<p>Deformations of a bent beam: (<b>a</b>) deformations in the longitudinal direction and (<b>b</b>) deformations on the beam’s cross section.</p>
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<p>(<b>a</b>) A diagram of the stress state and (<b>b</b>) stress distribution in the beam.</p>
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<p>A cantilever beam with the mass, m, distributed evenly along the entire span, l (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi mathvariant="normal">m</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mi mathvariant="normal">m</mi> <mo>/</mo> <mi mathvariant="normal">l</mi> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) SEM micrograph of interface between CFRP laminate, glue and plywood; (<b>b</b>) EDS spectrum and (<b>c</b>) EDS layered images for area shown in (<b>a</b>).</p>
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<p>EDS elemental mapping in the area shown in <a href="#materials-18-00207-f001" class="html-fig">Figure 1</a>a.</p>
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<p>(<b>a</b>) MOE and (<b>b</b>) MOR values obtained in three-point bending test.</p>
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<p>Deformation, ε, of CFRP-reinforced plywood sample measured using strain gauges (<b>a</b>) 2, (<b>b</b>) 1, (<b>c</b>) 4 and (<b>d</b>) 3.</p>
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<p>Deformation, ε, of unreinforced plywood sample measured using strain gauges (<b>a</b>) 2, (<b>b</b>) 1, (<b>c</b>) 4 and (<b>d</b>) 3.</p>
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<p>The values of tensile and compressive stresses obtained during measurements.</p>
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<p>Comparison of stress distribution and neutral axis position: (<b>a</b>) CFRP-reinforced plywood panel; (<b>b</b>) plywood.</p>
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<p>Plywood with 12 mm thickness: (<b>a</b>) panel and (<b>b</b>) arrangement of veneers.</p>
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<p>CFRP structure.</p>
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<p>Cross section of CFRP-reinforced plywood (plywood was used as back material).</p>
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<p>(<b>a</b>) Sample prepared for SEM analysis and (<b>b</b>) X-ray micrograph of CFRP-reinforced plywood laminate.</p>
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<p>Three-point bending test: (<b>a</b>) measuring stand, (<b>b</b>) measurement scheme (L = 240 mm) and (<b>c</b>) Megatron SPR18-100 sensor for measuring linear displacements.</p>
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<p>Measuring track for analysis of deformations and dynamic characteristics.</p>
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<p>Measurement of cantilever beam deformations: (<b>a</b>) measuring stand, (<b>b</b>) strain gauge and (<b>c</b>) measurement scheme.</p>
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<p>A block diagram of application for the determination of the natural frequency of sample vibrations in LabVIEW 2022.</p>
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<p>Equivalent loads acting on the considered element of infinitesimal length, dx.</p>
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<p>(<b>a</b>) Stress–strain tensile curve for CFRP panel and (<b>b</b>) sample after destruction.</p>
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<p>(<b>a</b>) Stress–strain tensile curve for 12 mm thick plywood and (<b>b</b>) sample after destruction.</p>
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<p>(<b>a</b>) Load–displacement curve (three-point bending test) for 12 mm thick plywood and (<b>b</b>) sample after failure.</p>
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<p>Three-point bending test results of CFRP-reinforced plywood sample.</p>
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<p>Time histories of strain amplitude of CFRP-reinforced plywood measured with (<b>a</b>) strain gauge no. 2 and (<b>b</b>) strain gauge no. 4.</p>
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<p>Time histories of strain amplitude of plywood measured with (<b>a</b>) strain gauge no. 2 and (<b>b</b>) strain gauge no. 4.</p>
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<p>Natural frequency of cantilever beam: (<b>a</b>) plywood; (<b>b</b>) CFRP-reinforced plywood.</p>
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22 pages, 2843 KiB  
Article
The Application of Structural Reliability and Sensitivity Analysis in Engineering Practice
by Urszula Radoń and Paweł Zabojszcza
Appl. Sci. 2025, 15(1), 342; https://doi.org/10.3390/app15010342 - 1 Jan 2025
Viewed by 371
Abstract
Standard safety assessments of civil engineering systems are conducted using safety factors. An alternative method to this approach is the assessment of the engineering system using reliability analysis of the structure. In reliability analysis of the structure, both the uncertainty of the load [...] Read more.
Standard safety assessments of civil engineering systems are conducted using safety factors. An alternative method to this approach is the assessment of the engineering system using reliability analysis of the structure. In reliability analysis of the structure, both the uncertainty of the load and the properties of the materials or geometry are explicitly taken into account. The uncertainties are described in a probabilistic manner. After defining the ultimate and serviceability limit state functions, we can calculate the failure probability for each state. When assessing structural reliability, it is useful to calculate measures that provide information about the influence of random parameters on the failure probability. Classical measures are vectors, whose coordinates are the first partial derivatives of reliability indices evaluated in the design point. These values are obtained as a by-product of the First-Order Reliability Method. Furthermore, we use Sobol indices to describe the sensitivity of the failure probability to input random variables. Computations of the Sobol indices are carried out using the classic Monte Carlo method. The aim of this article is not to define new sensitivity measures, but to show the advantages of using structural reliability and sensitivity analysis in everyday design practice. Using a simple cantilever beam as an example, we will present calculations of probability failure and local and global sensitivity measures. The calculations will be performed using COMREL modules of the STRUREL computing environment. Based on the results obtained from the sensitivity analysis, we can conclude that in the case of the serviceability limit state, the most significant influence on the results is exerted by variables related to the geometry of the beam under consideration. The influence of changes in Young’s modulus and load on the probability of failure is minimal. In further calculations, these quantities can be treated as deterministic. In the case of the ultimate limit state, the influence of changes in the yield strength is significant. The influence of changes in the load and length of the beam is significantly smaller. The authors present two alternative ways of designing with a probabilistic approach, using the FORM (SORM) and Monte Carlo simulation. The approximation FORM cannot be used in every case in connection with gradient determination problems. In such cases, it is worth using the Monte Carlo simulation method. The results of both methods are comparable. Full article
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<p>Illustration of limit state function g(<b>x</b>), safe area Ω<sub>s</sub>, and failure area Ω<sub>f</sub> for two random variables.</p>
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<p>Transformation of a limit state function to a standard Gaussian space.</p>
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<p>Concept of the Monte Carlo method.</p>
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<p>Illustration of the elasticity of reliability index β as a function of parameter p.</p>
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<p>Geometry and load of the cantilever beam.</p>
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<p>Graphical illustration of the coordinates of vector <b>α</b> for SLS.</p>
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<p>Graphical illustration of the elasticity of the reliability index based on mean value for SLS.</p>
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<p>Graphical illustration of the elasticity of the reliability index based on standard deviation for SLS.</p>
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<p>Graphical illustration of the coordinates of vector <b>α</b> for ULS.</p>
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<p>Graphical illustration of the elasticity of the reliability index based on mean value for ULS.</p>
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<p>Graphical illustration of the elasticity of the reliability index based on standard deviation for ULS.</p>
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23 pages, 7523 KiB  
Article
Fracture Toughness Assessment of Pipeline Steels Under Hydrogen Exposure for Blended Gas Applications
by Hesamedin Ghadiani, Zoheir Farhat, Tahrim Alam and Md. Aminul Islam
Metals 2025, 15(1), 29; https://doi.org/10.3390/met15010029 - 1 Jan 2025
Viewed by 451
Abstract
Hydrogen embrittlement (HE) is a critical concern for pipeline steels, particularly as the energy sector explores the feasibility of blending hydrogen with natural gas to reduce carbon emissions. Various mechanical testing methods assess HE, with fracture toughness testing offering a quantitative measure of [...] Read more.
Hydrogen embrittlement (HE) is a critical concern for pipeline steels, particularly as the energy sector explores the feasibility of blending hydrogen with natural gas to reduce carbon emissions. Various mechanical testing methods assess HE, with fracture toughness testing offering a quantitative measure of defect impacts on structural safety, particularly for cracks arising during manufacturing, fabrication, or in-service conditions. This study focuses on assessing the fracture toughness of two pipeline steels from an existing natural gas network under varying hydrogen concentrations using double cantilever beam (DCB) fracture tests. A vintage API X52 steel with a ferritic–pearlitic microstructure and a modern API X65 steel with polygonal ferrite and elongated pearlite colonies were selected to represent old and new pipeline materials. Electrochemical hydrogen charging was employed to simulate hydrogen exposure, with the charging parameters derived from hydrogen permeation tests. The results highlight the differing impacts of hydrogen on the fracture toughness and crack growth in vintage and modern pipeline steels. These findings are essential for ensuring the safety and integrity of pipelines carrying hydrogen–natural gas blends. Full article
(This article belongs to the Special Issue Hydrogen Embrittlement of Metals: Behaviors and Mechanisms)
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Figure 1
<p>(<b>a</b>) Sections of AO-C1 and N-C1 pipes; (<b>b</b>) specimen orientation.</p>
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<p>Microstructure of AO-C1 steel: (<b>a</b>) low magnification view; (<b>b</b>) higher magnification of the region highlighted by the red rectangle.</p>
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<p>Microstructure of N-C1 steel: (<b>a</b>) low magnification view; (<b>b</b>) higher magnification of the region highlighted by the red rectangle; (<b>c</b>) 3D profile of the marked pore in as-polished condition.</p>
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<p>XRD patterns of (<b>a</b>) AO-C1 steel and (<b>b</b>) N-C1 steel.</p>
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<p>DCB test specimen.</p>
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<p>Test setup for electrochemical hydrogen pre-charging.</p>
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<p>DCB fracture test setup.</p>
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<p>DCB fracture test results: K<sub>IHE</sub> versus C<sub>H</sub> for (<b>a</b>) AO-C1 steel and (<b>b</b>) N-C1 steel.</p>
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<p>DCB fracture test results: crack growth versus C<sub>H</sub> for (<b>a</b>) AO-C1 steel and (<b>b</b>) N-C1 steel.</p>
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<p>Fractography of uncharged N-C1 DCB specimen: (<b>a</b>) confocal image from side view before sidearm separation; (<b>b</b>) SEM image of the fracture surface after sidearm separation (green dashed line separates the DCB test region from post-test region); (<b>c</b>) magnification of red area marked by “c” (DCB test region); (<b>d</b>) magnification of red area marked by “d” (post-test region); (<b>e</b>) magnification of red area marked by “e” (lower magnification of the post-test region, better showing the dimple feature characteristic).</p>
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<p>Fractography of pre-charged (C<sub>H</sub> = 1.8 wppm) N-C1 DCB specimen: (<b>a</b>) confocal image from side view before sidearm separation; (<b>b</b>) SEM image of the fracture surface after sidearm separation (green dashed line separates the DCB test region from post-test region); (<b>c</b>) magnification of red area marked by “c” (DCB test region); (<b>d</b>) magnification of red area marked by “d” (post-test region).</p>
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27 pages, 7982 KiB  
Article
Contact Dynamic Behaviors of Magnetic Hydrogel Soft Robots
by Yunian Shen and Yiming Zou
Gels 2025, 11(1), 20; https://doi.org/10.3390/gels11010020 - 31 Dec 2024
Viewed by 265
Abstract
Magnetic hydrogel soft robots have shown great potential in various fields. However, their contact dynamic behaviors are complex, considering stick–slip motion at the contact interface, and lack accurate computational models to analyze them. This paper improves the numerical computational method for hydrogel materials [...] Read more.
Magnetic hydrogel soft robots have shown great potential in various fields. However, their contact dynamic behaviors are complex, considering stick–slip motion at the contact interface, and lack accurate computational models to analyze them. This paper improves the numerical computational method for hydrogel materials with magneto-mechanical coupling effect, analyses the inchworm-like contact motion of the biomimetic bipedal magnetic hydrogel soft robot, and designs and optimizes the robot’s structure. In the constitutive model, a correction factor representing the influence of the direction of magnetic flux density on the domain density has been introduced. The magnetic part of the Helmholtz free energy has been redefined as the magnetic potential energy, which can be used to explain the phenomenon that the material will still deform when the magnetic flux density is parallel to the external magnetic field. The accuracy of the simulation is verified by comparing numerical solutions with experimental results for a magnetic hydrogel cantilever beam. Furthermore, employing the present methods, the locomotion of a magnetic hydrogel soft robot modeled after the inchworm’s gait is simulated, and the influence of the coefficient of friction on its movement is discussed. The numerical results clearly display the control effect of the external magnetic field on the robot’s motion. Full article
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Figure 1
<p>Magnetic hysteresis loops of magnetic materials along certain direction (where <span class="html-italic">H</span> represents the projection of the magnetic field strength <b>H</b>, <span class="html-italic">B</span> represents the projection of the magnetic flux density <b>B</b>, <span class="html-italic">B</span> represents the projection of the coercivity <b>H</b><sup>c</sup>, <span class="html-italic">B</span><sup>m</sup> represents the projection of the saturation magnetic flux density <b>B</b><sup>m</sup>, and <span class="html-italic">B</span><sup>r</sup> represents the projection of the remanence of <b>B</b><sup>r</sup> along a certain direction).</p>
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<p>Schematic diagram of material line elements.</p>
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<p>Schematic diagram of the variation of magnetic domain density with the deformation of magnetic hydrogel.</p>
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<p>Curve of the rate of change of magnetic flux density <math display="inline"><semantics> <mrow> <msup> <mi>λ</mi> <mi mathvariant="normal">m</mi> </msup> </mrow> </semantics></math> versus the material stretch ratio <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>z</mi> </msub> </mrow> </semantics></math> in the same direction.</p>
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<p>Micro-element of equivalent continuum body.</p>
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<p>Uniaxial extension and compression of a cubic of magnetic hydrogel.</p>
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<p>Numerical solutions for displacement contour of the magnetic hydrogel cube in the <span class="html-italic">z</span> direction. (<b>a</b>) Initial undeformed state with no external magnetic field; (<b>b</b>) compressed deformation under the action of an external magnetic field (<span class="html-italic">λ<sub>z</sub></span> = 0.83); (<b>c</b>) extension state under the action of an external magnetic field (<span class="html-italic">λ<sub>z</sub></span> = 1.22).</p>
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<p>Uniaxial extension and compression of the magnetic hydrogel cube in the magnetic field.</p>
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<p>Schematic diagram of the magnetic hydrogel cantilever beam under the magnetic field force.</p>
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<p>Bending of the hydrogel cantilever beam: (<b>a</b>) deflection of the magnetic polyvinyl alcohol (PVA) hydrogel cantilever beam in the experiment under 30 mT; (<b>b</b>) deflection of the magnetic PVA hydrogel cantilever beam in the simulation under 30 mT; (<b>c</b>) comparison of experimental, theoretical, and simulation deflection results of the magnetic PVA cantilever beam under different external magnetic induction intensities.</p>
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<p>Schematic diagram of the double-feet magnetic hydrogel soft robot.</p>
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<p>Deformation and force of the designed bipedal magnetic hydrogel soft robot under the magnetic field. (<b>a</b>) The initial configuration of the soft robot, L is the foot length, is half of the foot angle, <b>B</b><sup>r</sup> is the residual magnetic flux density of the material, <b>B</b> is the magnetic flux density of the material in the instantaneous configuration, <math display="inline"><semantics> <mrow> <msup> <mstyle mathvariant="bold" mathsize="normal"> <mi>B</mi> </mstyle> <mrow> <mi>applied</mi> </mrow> </msup> </mrow> </semantics></math> is the external magnetic field strength applied, M is the center point of the structure, P is the contact point; (<b>b</b>) under the external magnetic field strength in the x-direction, the bipedal structure bends inward, and at this time, due to the different bending deflections of each point on the foot length, each point B is also different, thus generating different directions of forces on the two feet under the external magnetic field strength in the <span class="html-italic">z</span>-direction, and the rear foot lifts off the contact surface.</p>
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<p>Variation of magnetic field strength loads in the <span class="html-italic">x</span> and <span class="html-italic">z</span> directions over time.</p>
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<p>Schematic diagram of the magnetic bipedal hydrogel soft robot structure (where <span class="html-italic">W</span> is the width, <span class="html-italic">L</span> is the foot length, and <span class="html-italic">c</span> is the thickness).</p>
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<p>Model used for parameterized optimization.</p>
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<p>Displacement of the end of the foot structure in the <span class="html-italic">x</span>-direction for different peak values of magnetic field load of 80~240 mT and 1/2 bipedal angles of 20–55°.</p>
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<p>Schematic diagram of the soft robot’s motion within one cycle (Von Mises stress contour) compared with the motion of the inchworm. (<b>a</b>) The rear foot leaves the contact surface at 0.55 s; (<b>b</b>) the two feet complete the inward bending at 1.32 s; (<b>c</b>) the front foot leaves the contact surface at 2.33 s; (<b>d</b>) the motion cycle is completed.</p>
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<p>Displacement of the soft robot’s center point M in the <span class="html-italic">x</span> and <span class="html-italic">z</span> directions within one cycle.</p>
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<p>Velocity of the soft robot’s center point M in the <span class="html-italic">x</span> and <span class="html-italic">z</span> directions within one cycle.</p>
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<p>Time history of the displacement of the soft robot’s center point M in the <span class="html-italic">x</span> direction under different coefficients of friction.</p>
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35 pages, 15971 KiB  
Review
MEMS Acoustic Sensors: Charting the Path from Research to Real-World Applications
by Qingyi Wang, Yang Zhang, Sizhe Cheng, Xianyang Wang, Shengjun Wu and Xufeng Liu
Micromachines 2025, 16(1), 43; https://doi.org/10.3390/mi16010043 - 30 Dec 2024
Viewed by 298
Abstract
MEMS acoustic sensors are a type of physical quantity sensor based on MEMS manufacturing technology for detecting sound waves. They utilize various sensitive structures such as thin films, cantilever beams, or cilia to collect acoustic energy, and use certain transduction principles to read [...] Read more.
MEMS acoustic sensors are a type of physical quantity sensor based on MEMS manufacturing technology for detecting sound waves. They utilize various sensitive structures such as thin films, cantilever beams, or cilia to collect acoustic energy, and use certain transduction principles to read out the generated strain, thereby obtaining the targeted acoustic signal’s information, such as its intensity, direction, and distribution. Due to their advantages in miniaturization, low power consumption, high precision, high consistency, high repeatability, high reliability, and ease of integration, MEMS acoustic sensors are widely applied in many areas, such as consumer electronics, industrial perception, military equipment, and health monitoring. Through different sensing mechanisms, they can be used to detect sound energy density, acoustic pressure distribution, and sound wave direction. This article focuses on piezoelectric, piezoresistive, capacitive, and optical MEMS acoustic sensors, showcasing their development in recent years, as well as innovations in their structure, process, and design methods. Then, this review compares the performance of devices with similar working principles. MEMS acoustic sensors have been increasingly widely applied in various fields, including traditional advantage areas such as microphones, stethoscopes, hydrophones, and ultrasound imaging, and cutting-edge fields such as biomedical wearable and implantable devices. Full article
(This article belongs to the Special Issue Recent Advances in Silicon-Based MEMS Sensors and Actuators)
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<p>Classification of MEMS acoustic sensors based on different working principles.</p>
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<p>Piezoelectric MEMS acoustic sensors. (<b>a</b>) Basic working principle and typical multilayer structure of piezoelectric MEMS acoustic sensors. (<b>b</b>) A ZnO MEMS acoustic sensor with air cavity [<a href="#B29-micromachines-16-00043" class="html-bibr">29</a>]. (<b>c</b>) Multilayer cantilever design of a piezoelectric MEMS microphone, with AlN as piezoelectric material and MO as an electrode material [<a href="#B30-micromachines-16-00043" class="html-bibr">30</a>].</p>
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<p>Piezoelectric MEMS acoustic sensor based on ZnO film. (<b>a</b>) ZnO based structure for development of MEMS acoustic sensor [<a href="#B29-micromachines-16-00043" class="html-bibr">29</a>]. (<b>b</b>–<b>d</b>) The cavity structure with microtunnel design, which relates to the atmosphere, as a replacement of the traditional acoustic holes. (<b>b</b>) The fabricated cavity and metal electrode structure of ZnO MEMS acoustic sensor [<a href="#B48-micromachines-16-00043" class="html-bibr">48</a>]. (<b>c</b>) A ZnO MEMS acoustic sensor for aeroacoustic measurements [<a href="#B50-micromachines-16-00043" class="html-bibr">50</a>]. (<b>d</b>) A MEMS acoustic sensor with microtunnel for high SPL measurement, and with less risk of microtunnel blockages [<a href="#B51-micromachines-16-00043" class="html-bibr">51</a>].</p>
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<p>Piezoelectric MEMS acoustic sensor based on AlN. (<b>a</b>) A AlN pMUT based on the compatibility characteristics between AlN and CMOS processes [<a href="#B53-micromachines-16-00043" class="html-bibr">53</a>]. (<b>b</b>) AlN MEMS acoustic sensor aiming for ultra low working frequency [<a href="#B54-micromachines-16-00043" class="html-bibr">54</a>]. (<b>c</b>) AlN MEMS acoustic sensor with ultra-thin silicon substrate, and different structures for low and high working frequency [<a href="#B56-micromachines-16-00043" class="html-bibr">56</a>]. (<b>d</b>) AlN MEMS acoustic sensor with enhanced SNR (67.03 dB at 1 kHz) [<a href="#B22-micromachines-16-00043" class="html-bibr">22</a>]. (<b>e</b>) AlN MEMS hydrophone with high sensitivity (−178 dB, re. 1 V/μPa) and low noise density (52.6 dB@100 Hz, re. μPa/√Hz) [<a href="#B58-micromachines-16-00043" class="html-bibr">58</a>]. (<b>f</b>) AlN MEMS wideband (10 Hz to more than 10 kHz) acoustic sensor coated by organic film (elastic polyurethane) [<a href="#B59-micromachines-16-00043" class="html-bibr">59</a>].</p>
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<p>Piezoelectric MEMS hydrophone. (<b>a</b>) A face to face, cross-configuration of four cantilevers design [<a href="#B67-micromachines-16-00043" class="html-bibr">67</a>]. (<b>b</b>) Single cantilever beam design [<a href="#B68-micromachines-16-00043" class="html-bibr">68</a>].</p>
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<p>Wearable acoustic sensor based on piezoelectric method. (<b>a</b>) Air-silicone composite device for physiological sounds detection [<a href="#B69-micromachines-16-00043" class="html-bibr">69</a>,<a href="#B72-micromachines-16-00043" class="html-bibr">72</a>]. (<b>b</b>) MEMS bionic hydrophone for heart sound sensing [<a href="#B73-micromachines-16-00043" class="html-bibr">73</a>].</p>
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<p>Representative structure and working principle diagram of piezoresistive MEMS hydrophone.</p>
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<p>Piezoresistive MEMS acoustic sensor. (<b>a</b>) Low-frequency-detectable acoustic sensor using a piezoresistive cantilever [<a href="#B57-micromachines-16-00043" class="html-bibr">57</a>]. (<b>b</b>) Frequency-specific highly sensitive acoustic sensor using a piezoresistive cantilever and parallel Helmholtz resonators [<a href="#B81-micromachines-16-00043" class="html-bibr">81</a>].</p>
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<p>Piezoresistive hydrophones with cilium structure. (<b>a</b>) Traditional cilium design in piezoresistive hydrophones [<a href="#B88-micromachines-16-00043" class="html-bibr">88</a>]. (<b>b</b>) CCVH: cilia cluster vector hydrophone [<a href="#B85-micromachines-16-00043" class="html-bibr">85</a>]. (<b>c</b>) DCVH: dumbbell-shaped ciliary vector hydrophone [<a href="#B86-micromachines-16-00043" class="html-bibr">86</a>]. (<b>d</b>) HCVH: hollow cilium cylinder vector hydrophone [<a href="#B87-micromachines-16-00043" class="html-bibr">87</a>]. (<b>e</b>) BCVH: beaded cilia MEMS vector hydrophone [<a href="#B88-micromachines-16-00043" class="html-bibr">88</a>]. (<b>f</b>) CSCVH: cap-shaped ciliary vector hydrophone [<a href="#B89-micromachines-16-00043" class="html-bibr">89</a>]. (<b>g</b>) SCVH: sculpture-shape cilium MEMS vector hydrophone [<a href="#B90-micromachines-16-00043" class="html-bibr">90</a>]. (<b>h</b>) CCCVH: crossed-circle cilium vector hydrophone [<a href="#B91-micromachines-16-00043" class="html-bibr">91</a>].</p>
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<p>Piezoresistive hydrophones with multiple cilium structure. (<b>a</b>,<b>b</b>) FUVH: four-unit MEMS vector hydrophone [<a href="#B93-micromachines-16-00043" class="html-bibr">93</a>,<a href="#B95-micromachines-16-00043" class="html-bibr">95</a>]. (<b>c</b>) FUVH with annulus-shaped structure [<a href="#B94-micromachines-16-00043" class="html-bibr">94</a>].</p>
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<p>Representative structure and working principle diagram of capacitive MEMS acoustic sensors.</p>
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<p>Capacitive MEMS Microphone. (<b>a</b>) Low-power digital capacitive MEMS microphone based on a triple-sampling delta-sigma ADC with embedded gain [<a href="#B101-micromachines-16-00043" class="html-bibr">101</a>]. (<b>b</b>) Wearable capacitive MEMS microphone for cardiac monitoring at the wrist [<a href="#B102-micromachines-16-00043" class="html-bibr">102</a>]. (<b>c</b>) Capacitive MEMS stethoscope with anti-stiction-dimple array design in the diaphragm and the backplate for highly reliable heart or lung sounds detection [<a href="#B105-micromachines-16-00043" class="html-bibr">105</a>].</p>
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<p>Capacitive MEMS microphone with biomimetic design. (<b>a</b>) Dual-band MEMS directional acoustic sensor for near-resonance operation [<a href="#B110-micromachines-16-00043" class="html-bibr">110</a>]. (<b>b</b>) Directional-resonant MEMS acoustic sensor and associated acoustic vector sensor [<a href="#B111-micromachines-16-00043" class="html-bibr">111</a>]. Both (<b>a</b>,<b>b</b>) are inspired by the tympana configuration of the parasitic fly <span class="html-italic">Ormia ochracea</span>. The circled numbers in (<b>b</b>) are used to distinguish different structures.</p>
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<p>MEMS acoustic sensor based on optical grating interferometer. (<b>a</b>) A grating interferometer design by a diffraction grating integrated backplate and a pressure-sensitive diaphragm [<a href="#B117-micromachines-16-00043" class="html-bibr">117</a>]. (<b>b</b>) Design of a MEMS optical microphone transducer based on light phase modulation [<a href="#B120-micromachines-16-00043" class="html-bibr">120</a>]. (<b>c</b>) Grating interferometer design with short-cavity structure and grating-on-convex-platform structure [<a href="#B118-micromachines-16-00043" class="html-bibr">118</a>,<a href="#B119-micromachines-16-00043" class="html-bibr">119</a>].</p>
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<p>MEMS acoustic sensor based on Fabry–Perot method. (<b>a</b>) A typical structure of Fabry–Perot MEMS acoustic sensors. (<b>b</b>) An acoustic sensor based on active fiber Fabry–Pérot microcavities [<a href="#B21-micromachines-16-00043" class="html-bibr">21</a>]. (<b>c</b>) An application in the detection and position of partial discharge [<a href="#B122-micromachines-16-00043" class="html-bibr">122</a>].</p>
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<p>Applications of MEMS acoustic sensors in biomedical field.</p>
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27 pages, 28870 KiB  
Article
A Novel Procedure in Scrutinizing a Cantilever Beam with Tip Mass: Analytic and Bifurcation
by Asma Alanazy, Galal M. Moatimid, T. S. Amer, Mona A. A. Mohamed and M. K. Abohamer
Axioms 2025, 14(1), 16; https://doi.org/10.3390/axioms14010016 - 30 Dec 2024
Viewed by 257
Abstract
An examination was previously derived to conclude the understanding of the response of a cantilever beam with a tip mass (CBTM) that is stimulated by a parameter to undergo small changes in flexibility (stiffness) and tip mass. The study of this problem is [...] Read more.
An examination was previously derived to conclude the understanding of the response of a cantilever beam with a tip mass (CBTM) that is stimulated by a parameter to undergo small changes in flexibility (stiffness) and tip mass. The study of this problem is essential in structural and mechanical engineering, particularly for evaluating dynamic performance and maintaining stability in engineering systems. The existing work aims to study the same problem but in different situations. He’s frequency formula (HFF) is utilized with the non-perturbative approach (NPA) to transform the nonlinear governing ordinary differential equation (ODE) into a linear form. Mathematica Software 12.0.0.0 (MS) is employed to confirm the high accuracy between the nonlinear and the linear ODE. Actually, the NPA is completely distinct from any traditional perturbation technique. It simply inspects the stability criteria in both the theoretical and numerical calculations. Temporal histories of the obtained results, in addition to the corresponding phase plane curves, are graphed to explore the influence of various parameters on the examined system’s behavior. It is found that the NPA is simple, attractive, promising, and powerful; it can be adopted for the highly nonlinear ODEs in different classes in dynamical systems in addition to fluid mechanics. Bifurcation diagrams, phase portraits, and Poincaré maps are used to study the chaotic behavior of the model, revealing various types of motion, including periodic and chaotic behavior. Full article
(This article belongs to the Special Issue Applied Nonlinear Dynamical Systems in Mathematical Physics)
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Figure 1
<p>The graphical representation of the cantilever beam.</p>
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<p>A comparison between the numerical results of the CBTM Equation (1) and the equivalent one (6).</p>
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<p>The temporal histories of the solution <math display="inline"><semantics> <mi>u</mi> </semantics></math> of Equation (6) according to the NPA when (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>η</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mn>0.5</mn> <mo>,</mo> <mn>0.8</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>β</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.5</mn> <mo>,</mo> <mn>0.8</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>1.6</mn> <mo>,</mo> <mn>1.7</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.2</mn> <mo>,</mo> <mn>0.3</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>2.5</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, and (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.3</mn> <mo>,</mo> <mn>0.4</mn> <mo>,</mo> <mn>0.5</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>The corresponding curves of <a href="#axioms-14-00016-f003" class="html-fig">Figure 3</a> in the plane <math display="inline"><semantics> <mrow> <mi>u</mi> <mtext> </mtext> <mover accent="true"> <mi>u</mi> <mo>˙</mo> </mover> </mrow> </semantics></math> at (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>η</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mn>0.5</mn> <mo>,</mo> <mn>0.8</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>β</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.5</mn> <mo>,</mo> <mn>0.8</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>1.6</mn> <mo>,</mo> <mn>1.7</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.2</mn> <mo>,</mo> <mn>0.3</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>2.5</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, and (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.3</mn> <mo>,</mo> <mn>0.4</mn> <mo>,</mo> <mn>0.5</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>The stability areas of the damped CBTM with the diverse values of <math display="inline"><semantics> <mi>η</mi> </semantics></math>.</p>
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<p>The stability areas of the CBTM with the diverse values of <math display="inline"><semantics> <mi>q</mi> </semantics></math>.</p>
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<p>The stability areas of the CBTM with the diverse values of <math display="inline"><semantics> <mi>β</mi> </semantics></math>.</p>
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<p>The stability areas of the CBTM with the distinct amounts of <math display="inline"><semantics> <mi>σ</mi> </semantics></math>.</p>
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<p>The stability zones of the CBTM with the diverse values of <math display="inline"><semantics> <mi>ω</mi> </semantics></math>.</p>
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<p>The stability regions of the CBTM with the diverse values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>A comparison between the numerical results of the un-damped CBTM Equation (17) and the NPA Equation (20).</p>
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<p>The temporal history of the solution of the NPA Equation (20) when (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>2.5</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.2</mn> <mo>,</mo> <mn>0.3</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>1.6</mn> <mo>,</mo> <mn>1.7</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.3</mn> <mo>,</mo> <mn>0.4</mn> <mo>,</mo> <mn>0.6</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>The phase plane curves for the related ones in <a href="#axioms-14-00016-f012" class="html-fig">Figure 12</a> when (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>2.5</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.2</mn> <mo>,</mo> <mn>0.3</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mn>1.6</mn> <mo>,</mo> <mn>1.7</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mtext> </mtext> <mo stretchy="false">(</mo> <mo>=</mo> <mn>0.3</mn> <mo>,</mo> <mn>0.4</mn> <mo>,</mo> <mn>0.6</mn> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>The stability areas in the un-damped state with the varied values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>The stability areas in the un-damped state with the varied values of <math display="inline"><semantics> <mi>σ</mi> </semantics></math>.</p>
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<p>The stability areas in the un-damped state with the varied values of <math display="inline"><semantics> <mi>q</mi> </semantics></math>.</p>
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<p>The stability areas in the un-damped state with the varied values of <math display="inline"><semantics> <mi>ω</mi> </semantics></math>.</p>
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<p>The PolarPlot of <math display="inline"><semantics> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for different measures of the excited amplitude <math display="inline"><semantics> <mi>q</mi> </semantics></math>.</p>
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<p>The PolarPlot of <math display="inline"><semantics> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for different measures of the excited frequency <math display="inline"><semantics> <mi>σ</mi> </semantics></math>.</p>
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<p>The PolarPlot of <math display="inline"><semantics> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for different measures of the natural frequency <math display="inline"><semantics> <mi>ω</mi> </semantics></math>.</p>
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<p>The Polar Plot of <math display="inline"><semantics> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> for various measures of the initial amplitude <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
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<p>Bifurcation diagram when the excitation amplitude varies.</p>
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<p>Phase portraits (blue curves) and Poincaré maps (red dots) for different values of <math display="inline"><semantics> <mi>q</mi> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>3.5</mn> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>4.0</mn> </mrow> </semantics></math>.</p>
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<p>Bifurcation diagram as the frequency varies, and phase portraits and Poincaré maps at (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> when (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>6.0</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>5.17</mn> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
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18 pages, 5086 KiB  
Article
Analyzing the Vibration Response of Adhesively Bonded Composite Cantilevers
by Jarosław Chełmecki, Paweł Szeptyński, Dorota Jasińska and Arkadiusz Kwiecień
Materials 2025, 18(1), 93; https://doi.org/10.3390/ma18010093 - 29 Dec 2024
Viewed by 303
Abstract
In this study, we investigated the vibration of adhesively bonded composite cantilevers consisting of two beech wood lamella and a bondline of flexible polyurethane. The beams had a constant total height, while the thickness of the adhesive layer varied. We analyzed both the [...] Read more.
In this study, we investigated the vibration of adhesively bonded composite cantilevers consisting of two beech wood lamella and a bondline of flexible polyurethane. The beams had a constant total height, while the thickness of the adhesive layer varied. We analyzed both the driven and free vibration of a single cantilever beam and a cantilever with an additional mass attached to its end. The eigenfrequencies were determined using Fourier analysis of a sweep load response, the response to an impact load excited using an impact hammer, and the response observed via the manual displacement of the beam’s tip. The system’s damping was estimated according to the recorded logarithmic decrement. Theoretical estimates of the fundamental natural frequency were obtained using the γ-method and employing a linear elastic theory of composite beams. A numerical modal analysis was carried out using the finite element method. Upon comparing the results of our experiments with the numerical estimates and theoretical predictions, a fair agreement was found. Full article
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<p>Geometry of the specimens.</p>
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<p>(<b>a</b>) Laboratory setup; (<b>b</b>) fixing of the specimen to the shake table.</p>
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<p>Laboratory setup for static four-point bending test.</p>
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<p>(<b>a</b>) Discrete mass model (<b>b</b>) Flexibility coefficients as displacements corresponding with a unit point load.</p>
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<p>Fundamental eigenfrequencies and vibration modes in two perpendicular directions, Y and Z.</p>
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<p>Accelerogram corresponding with B/2/S/10–17/100% test.</p>
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<p>Accelerogram corresponding to B/2/I/HT test.</p>
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<p>Fourier frequency spectrum corresponding to B/2/S/10–17/100% test.</p>
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<p>Fourier frequency spectrum corresponding to B/2/I/HT test.</p>
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<p>Measured and predicted fundamental frequencies of adhesively bonded beams.</p>
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15 pages, 4490 KiB  
Article
Non-Destructive Testing for Evaluation of Young’s Modulus by Using Free Vibration Response of Composite Materials
by Mirela-Roxana Apsan, Ana-Maria Mitu, Catalin-Andrei Neagoe, Nicolae Pop and Tudor Sireteanu
Appl. Sci. 2025, 15(1), 189; https://doi.org/10.3390/app15010189 - 28 Dec 2024
Viewed by 550
Abstract
This article presents a non-destructive method, based on the response to free vibrations, which can be used with efficiency and reliability to determine the Young’s modulus of polymer composite materials reinforced with natural or synthetic fibers. The non-destructive tests are carried out by [...] Read more.
This article presents a non-destructive method, based on the response to free vibrations, which can be used with efficiency and reliability to determine the Young’s modulus of polymer composite materials reinforced with natural or synthetic fibers. The non-destructive tests are carried out by measuring the frequencies of bending free vibrations of cantilever beams with additional masses. By using inverse methods, the experimental values of elasticity modulus E are assessed and validated by numerical simulation, using the finite element method (FEM). For FEM modeling, the materials are considered linear, homogeneous, isotropic, and viscoelastic. Full article
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Figure 1
<p>Experimental setup.</p>
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<p>Schematic of the experimental setup.</p>
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<p>(<b>a</b>) Free vibration time records for composite specimens with hemp fibers; (<b>b</b>) Amplitude spectra for composite specimens with hemp fibers.</p>
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<p>(<b>a</b>) Free vibration time records for composite specimens with coconut fibers; (<b>b</b>) Amplitude spectra for composite specimens with coconut fibers.</p>
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<p>Plots of experimental data and their fit by analytical model.</p>
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<p>Comparison of free vibration time records and analytical fit by viscoelastic model with (<b>a</b>) hemp fibers; (<b>b</b>) coconut fibers.</p>
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<p>Plots of numerical results (FEM) and their fit by analytical model.</p>
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<p>Comparison of analytical model of experimental and FEM data in the case of hemp fibers.</p>
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<p>Comparison of analytical model of experimental and FEM data in the case of coconut fibers.</p>
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14 pages, 7150 KiB  
Article
The Effect of Metal Shielding Layer on Electrostatic Attraction Issue in Glass–Silicon Anodic Bonding
by Wenqi Yang, Yong Ruan and Zhiqiang Song
Micromachines 2025, 16(1), 31; https://doi.org/10.3390/mi16010031 - 28 Dec 2024
Viewed by 372
Abstract
Silicon–glass anode bonding is the key technology in the process of wafer-level packaging for MEMS sensors. During the anodic bonding process, the device may experience adhesion failure due to the influence of electric field forces. A common solution is to add a metal [...] Read more.
Silicon–glass anode bonding is the key technology in the process of wafer-level packaging for MEMS sensors. During the anodic bonding process, the device may experience adhesion failure due to the influence of electric field forces. A common solution is to add a metal shielding layer between the glass substrate and the device. In order to solve the problem of device failure caused by the electrostatic attraction phenomenon, this paper designed a double-ended solidly supported cantilever beam parallel plate capacitor structure, focusing on the study of the critical size of the window opening in the metal layer for the electric field shielding effect. The metal shield consists of 400 Å of Cr and 3400 Å of Au. Based on theoretical calculations, simulation analysis, and experimental testing, it was determined that the critical size for an individual opening in the metal layer is 180 μm × 180 μm, with the movable part positioned 5 μm from the bottom, which does not lead to failure caused by stiction due to electrostatic pull-in of the detection structure. It was proven that the metal shielding layer is effective in avoiding suction problems in secondary anode bonding. Full article
(This article belongs to the Special Issue Recent Advances in Silicon-Based MEMS Sensors and Actuators)
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Figure 1
<p>The overall structure of glass–silicon wafer-level packaging.</p>
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<p>Silicon–glass anodic bonding.</p>
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<p>(<b>a</b>) Glass sheet before secondary bonding; (<b>b</b>) glass sheet after secondary bonding; (<b>c</b>) morphology at a single window; (<b>d</b>) morphology at windows.</p>
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<p>A simple detection structure equivalent to the resonator structure.</p>
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<p>Simulation of electric potential (<b>a</b>) without a window and (<b>b</b>) with a 180 μm × 180 μm window.</p>
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<p>(<b>a</b>) The relationship between the window edge length and the potential difference (V) between the device and the substrate. (<b>b</b>) The relationship between the window edge length and the device deformation size.</p>
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<p>(<b>a</b>) Displacement of the electrostatic force of the device with a window size of 173 μm; (<b>b</b>) displacement of the device with an electrostatic force at a window size of 174 μm.</p>
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<p>Structure without a metal shield and with a metal shield (<b>a</b>); simple detection structure (<b>b</b>); movable part without comb fingers (<b>c</b>).</p>
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<p>Morphologies of (<b>a</b>) the simple structure, (<b>b</b>) the comb-free movable structure, and (<b>c</b>) the resonator structure after secondary bonding without a metal shield.</p>
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<p>Structures with the addition of a metal shield after secondary bonding: before being pushed and after being pushed by a probe for (<b>a</b>) the simple structure, (<b>b</b>) the resonator structure without combs, and (<b>c</b>) the resonator structure with combs.</p>
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<p>Observation of the different quantities and morphologies of metal-layer windows through the glass substrate side: (<b>a</b>) 25 windows, (<b>b</b>) 20 windows, (<b>c</b>) 15 windows, (<b>d</b>) 4 windows.</p>
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<p>The black substance on the metal layer after secondary anodic bonding. (<b>a</b>) Structure with 4 windows in the center (<b>b</b>) Structure with 4 windows around the edges</p>
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<p>(<b>a</b>) Microscope view of the movable part of the comb-free structure from the substrate side; (<b>b</b>) microscope view of the resonator structure from the substrate side.</p>
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<p>(<b>a</b>) The probe cannot be pushed when the window edge length is 190 μm; (<b>b</b>) the probe can be pushed when the window edge length is 180 μm. As shown by the arrow in the figure, the probe pushes forward, but the movable structure remains immobile.</p>
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25 pages, 11322 KiB  
Article
A Triboelectric Nanogenerator Utilizing a Crank-Rocker Mechanism Combined with a Spring Cantilever Structure for Efficient Energy Harvesting and Self-Powered Sensing Applications
by Xinhua Wang, Xiangjie Xu, Tao Sun and Gefan Yin
Electronics 2024, 13(24), 5032; https://doi.org/10.3390/electronics13245032 - 21 Dec 2024
Viewed by 312
Abstract
With the advancement of industrial automation, vibrational energy generated by machinery during operation is often underutilized. Developing efficient devices for vibration energy harvesting is thus essential. Triboelectric nanogenerators (TENGs) based on spring and cantilever beam structures show considerable potential for industrial vibration energy [...] Read more.
With the advancement of industrial automation, vibrational energy generated by machinery during operation is often underutilized. Developing efficient devices for vibration energy harvesting is thus essential. Triboelectric nanogenerators (TENGs) based on spring and cantilever beam structures show considerable potential for industrial vibration energy harvesting; however, traditional designs often fail to fully harness vibrational energy due to their structural limitations. This study proposes a triboelectric nanogenerator (TENG) based on a crank-rocker mechanism and a spring cantilever structure (CR-SC TENG), which combines a crank-rocker mechanism with a spring cantilever structure, designed for both energy harvesting and self-powered sensing. The CR-SC TENG incorporates a spring cantilever beam, a crank-rocker mechanism, and lever amplification principles, enabling it to respond sensitively to low-frequency, small-amplitude vibrations. Utilizing the crank-rocker and lever effects, this device significantly amplifies micro-amplitudes, enhancing energy capture efficiency and making it well suited for low-amplitude, complex industrial environments. Experimental results demonstrate that this design effectively amplifies micro-vibrations and markedly improves energy conversion efficiency within a frequency range of 1–35 Hz and an amplitude range of 1–3 mm. As a sensor, the CR-SC TENG’s dual-generation units produce output signals that precisely reflect vibration frequencies, making it suitable for the intelligent monitoring of industrial equipment. When placed on an air compressor operating at 25 Hz, the first-generation unit achieved an output voltage of 150 V and a current of 8 μA, while the second-generation unit produced an output voltage of 60 V and a current of 5 μA. These findings suggest that the CR-SC TENG, leveraging spring cantilever beams, crank-rocker mechanisms, and lever amplification, has significant potential for micro-amplitude energy harvesting and could play a key role in smart manufacturing, intelligent factories, and the Internet of Things. Full article
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<p>Application scenarios and fabrication of the CR-SC TENG. (<b>a</b>) Application scenarios of the CR-SC TENG; (<b>b</b>) installation of the CR-SC TENG on an air compressor; (<b>c</b>) structural composition of the CR-SC TENG; (<b>d</b>) real-life images of the CR-SC TENG components; (<b>e</b>) fully assembled structure of the CR-SC TENG.</p>
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<p>Fabrication and analysis of TiO<sub>2</sub>-FGSF. (<b>a</b>) Fabrication process of TiO<sub>2</sub>-FGSF; (<b>b</b>) schematic of the experimental triboelectric nanogenerator; (<b>c</b>) vibration testing platform; (<b>d</b>) open-circuit voltage for different doping ratios; (<b>e</b>) short-circuit current for different doping ratios; (<b>f</b>) output voltage and current under various loads; (<b>g</b>) output power under various loads.</p>
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<p>Working principle of the CR-SC TENG. (<b>a</b>) Vertical contact separation mode power generation principle (first power generation unit); (<b>b</b>) simulation of the power generation principle in contact separation mode; (<b>c</b>) schematic of the freestanding sliding mode (second power generation unit); (<b>d</b>) power generation principle of the freestanding sliding mode; (<b>e</b>) simulation of the freestanding sliding mode during operation.</p>
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<p>Physical model of the CR-SC TENG. (<b>a</b>) Schematic of the physical model of the CR-SC TENG; (<b>b</b>) schematic of the spring cantilever section model; (<b>c</b>) equivalent physical model of the CR-SC TENG; (<b>d</b>) crank-rocker mechanism model; (<b>e</b>) lever amplification model.</p>
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<p>Output performance of the CR-SC TENG with different structural parameters. (<b>a</b>) Schematic of the experimental platform; (<b>b</b>) simplified schematic of the CR-SC TENG structure; (<b>c</b>) effect of spring parameters on Voc; (<b>d</b>) effect of crank length on Voc; (<b>e</b>) effect of connecting rod length on Voc; (<b>f</b>) effect of rocker (driving arm) length on Voc; (<b>g</b>) effect of distance from the cantilever base to the frame base’s upper surface (distance between the first friction layers) on Voc; (<b>h</b>) effect of distance between the sliding rod and frame side (distance between the second friction layers) on Vocc; (<b>i</b>) effect of additional magnetic sheet mass on Vocc.</p>
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<p>Output performance of the CR-SC TENG under various external excitation conditions. (<b>a</b>) Experimental platform for testing the output of the CR-SC TENG; (<b>b</b>) open-circuit voltage of the first output unit of the CR-SC TENG as a function of frequency under different acceleration levels; (<b>c</b>) short-circuit current of the first output unit of the CR-SC TENG as a function of frequency under different acceleration levels; (<b>d</b>) open-circuit voltage of the second output unit of the CR-SC TENG as a function of frequency under different acceleration levels; (<b>e</b>) short-circuit current of the second output unit of the CR-SC TENG as a function of frequency under different acceleration levels.</p>
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<p>Practical applications of the CR-SC TENG. (<b>a</b>) Operation of the CR-SC TENG on an air compressor; (<b>b</b>) open-circuit voltage and short-circuit current outputs of the first triboelectric nanogenerator unit; (<b>c</b>) open-circuit voltage and short-circuit current outputs of the second triboelectric nanogenerator unit; (<b>d</b>) CR-SC TENG powering 118 LED lights; (<b>e</b>) FFT result of the open-circuit voltage signal from the first triboelectric nanogenerator unit; (<b>f</b>) FFT result of the open-circuit voltage signal from the second triboelectric nanogenerator unit; (<b>g</b>) power management circuit for the triboelectric nanogenerator; (<b>h</b>) output voltage variation in the CR-SC TENG with the power management circuit.</p>
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<p>Application of the CR-SC TENG as a self-powered vibration sensor. (<b>a</b>) Demonstration of the CR-SC TENG application on industrial equipment; (<b>b</b>) schematic diagram of the wireless monitoring module; (<b>c</b>) display on the host computer app (Bluetooth app for Triboelectric Nanogenerator Voltage Monitoring; (<b>d</b>) open-circuit voltage monitored at different frequencies using an oscilloscope; (<b>e</b>) open-circuit voltage monitored at different frequencies using the wireless monitoring module; (<b>f</b>) comparison of open-circuit voltage measurements from the oscilloscope and the wireless monitoring module.</p>
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19 pages, 1249 KiB  
Article
Dynamic Stiffness for a Levinson Beam Embedded Within a Pasternak Medium Subjected to Axial Load at Both Ends
by Zhijiang Chen, Qian Cheng, Xiaoqing Jin and Feodor M. Borodich
Buildings 2024, 14(12), 4008; https://doi.org/10.3390/buildings14124008 - 17 Dec 2024
Viewed by 580
Abstract
This work presents accurate values for the dynamic stiffness matrix coefficients of Levinson beams under axial loading embedded in a Winkler–Pasternak elastic foundation. Levinson’s theory accounts for greater shear deformation than the Euler–Bernoulli or Timoshenko theories. Using the dynamic stiffness approach, an explicit [...] Read more.
This work presents accurate values for the dynamic stiffness matrix coefficients of Levinson beams under axial loading embedded in a Winkler–Pasternak elastic foundation. Levinson’s theory accounts for greater shear deformation than the Euler–Bernoulli or Timoshenko theories. Using the dynamic stiffness approach, an explicit algebraic expression is derived from the homogeneous solution of the governing equations. The dynamic stiffness matrix links forces and displacements at the beam’s ends. The Wittrick–Williams algorithm solves the eigenvalue problem for the free vibration and buckling of uniform cross-section parts. Numerical results are validated against published data, and reliability is confirmed through consistency tests. Parametric studies explore the effects of aspect ratio, boundary conditions, elastic medium parameters, and axial force on beam vibration properties. The relative deviation for the fundamental frequency is almost 6.89% for a cantilever beam embedded in the Pasternak foundation, 5.16% for a fully clamped beam, and 4.79% for a clamped–hinged beam. Therefore, Levinson beam theory can be used for calculations relevant to loads with short durations that generate transient responses, such as impulsive loads from high-speed railways, using the mode superposition method. Full article
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<p>Deformation of (<b>a</b>) Winkler and (<b>b</b>) Pasternak foundation mechanical models.</p>
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<p>(<b>a</b>) Beam on Pasternak foundation. (<b>b</b>) Definition of positive forces, moments, and loads on beam element.</p>
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<p>Homogenous solution type and associated relative value of parameters <math display="inline"><semantics> <mi>δ</mi> </semantics></math> and <math display="inline"><semantics> <mi>η</mi> </semantics></math>.</p>
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<p>The dimensionless first natural frequency of the Levinson beam varies with the Winkler–Pasternak foundation parameters <math display="inline"><semantics> <msub> <mi>K</mi> <mi>W</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>K</mi> <mi>P</mi> </msub> </semantics></math>, the axial force, the slenderness ratio, and different boundary conditions: (<b>a</b>) cantilever; (<b>b</b>) simple supported; (<b>c</b>) clamped; (<b>d</b>) clamped–simple supported.</p>
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<p>The first three mode shape of cantilever Levinson beam embedded in elastic base (Winkler <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>W</mi> </msub> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>, Pasternak <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>W</mi> </msub> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mi>P</mi> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>) with <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <mi>h</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> subjected to different axial force: (<b>a</b>) 1st mode; (<b>b</b>) 2nd mode; (<b>c</b>) 3rd mode.</p>
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1 pages, 24225 KiB  
Article
Multiscale Concurrent Topology Optimization and Mechanical Property Analysis of Sandwich Structures
by Zihao Li, Shiqiang Li and Zhihua Wang
Materials 2024, 17(24), 6086; https://doi.org/10.3390/ma17246086 - 12 Dec 2024
Viewed by 588
Abstract
Based on the basic theoretical framework of the Bi-directional Evolutionary Structural Optimization method (BESO) and the Solid Isotropic Material with Penalization method (SIMP), this paper presents a multiscale topology optimization method for concurrently optimizing the sandwich structure at the macro level and the [...] Read more.
Based on the basic theoretical framework of the Bi-directional Evolutionary Structural Optimization method (BESO) and the Solid Isotropic Material with Penalization method (SIMP), this paper presents a multiscale topology optimization method for concurrently optimizing the sandwich structure at the macro level and the core layer at the micro level. The types of optimizations are divided into macro and micro concurrent topology optimization (MM), macro and micro gradient concurrent topology optimization (MMG), and macro and micro layered gradient concurrent topology optimization (MMLG). In order to compare the multiscale optimization method with the traditional macroscopic optimization method, the sandwich simply supported beam is illustrated as a numerical example to demonstrate the functionalities and superiorities of the proposed method. Moreover, several samples are printed through micro-nano 3D printing technology, and then the static three-point bending experiments and the numerical simulations are carried out. The mechanical properties of the optimized structures in terms of deformation modes, load-bearing capacity, and energy absorption characteristics are compared and analyzed in detail. Finally, the multiscale optimization methods are extended to the design of 2D sandwich cantilever beams and 3D sandwich fully clamped beams. Full article
(This article belongs to the Section Advanced Materials Characterization)
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<p>A 2D two-scale structure.</p>
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<p>2D rectangular base cell model.</p>
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<p>Flowchart of multiscale concurrent topology optimization.</p>
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<p>Optimization model and initial microstructure, (<b>a</b>) initial optimization model of sandwich simply supported beam, (<b>b</b>) initial microstructure.</p>
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<p>MM structure optimization history. (<b>a</b>) Macrostructure optimization history chart, (<b>b</b>) microstructure optimization history chart.</p>
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<p>MMG structure optimization history. (<b>a</b>) Macrostructure optimization history chart. (<b>b</b>) Microstructure optimization history chart.</p>
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<p>MMG structure topology optimization result.</p>
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<p>MMLG structure topology optimization.</p>
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<p>MMLG structure topology optimization history. (<b>a</b>) Macrostructure optimization history chart. (<b>b</b>) Microstructure optimization history chart.</p>
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<p>MMLG structure topology optimization result.</p>
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<p>Comparison of efficiency of different multiscale concurrent topology optimization algorithms [<a href="#B31-materials-17-06086" class="html-bibr">31</a>,<a href="#B38-materials-17-06086" class="html-bibr">38</a>,<a href="#B50-materials-17-06086" class="html-bibr">50</a>,<a href="#B51-materials-17-06086" class="html-bibr">51</a>,<a href="#B52-materials-17-06086" class="html-bibr">52</a>].</p>
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<p>Optimization design and initial microstructure. (<b>a</b>) Initial optimization model of sandwich simply supported beam. (<b>b</b>) Initial microstructure.</p>
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<p>MMG structure topology optimization result.</p>
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<p>MMLG structure topology optimization result.</p>
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<p>A 3D fully clamped beam structure.</p>
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<p>MM structure topology optimization result.</p>
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<p>MMG structure topology optimization result (the volume fraction of five microstructures varies from large to small, with values of 1, 0.8, 0.6, 0.4, and 0.2).</p>
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<p>MMLG structure topology optimization result.</p>
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<p>3D printing model preparation and results. (<b>a</b>) Printing direction. (<b>b</b>) Finished product status. (<b>c</b>) M structure. (<b>d</b>) MM structure. (<b>e</b>) MMG structure. (<b>f</b>) MMLG structure.</p>
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<p>(<b>a</b>) Material stress–strain curve. (<b>b</b>) Load displacement curve of 5 structures.</p>
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<p>Comparison of experimental and numerical deformation modes of 5 structures.</p>
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<p>(<b>a</b>) Comparison of force–displacement curves between experimental and numerical values of five structures. (<b>b</b>) Comparison of peak force and effective bearing displacement of five structures.</p>
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<p>Displacement of 5 structures. (<b>a</b>) S structure specimen displacement. (<b>b</b>) M structure specimen displacement. (<b>c</b>) MM structure specimen displacement. (<b>d</b>) MMG structure specimen displacement. (<b>e</b>) MMLG structure specimen displacement.</p>
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<p>Displacement of 5 structures. (<b>a</b>) S structure specimen displacement. (<b>b</b>) M structure specimen displacement. (<b>c</b>) MM structure specimen displacement. (<b>d</b>) MMG structure specimen displacement. (<b>e</b>) MMLG structure specimen displacement.</p>
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<p>Deformation modes of 4 structural specimens: (<b>a</b>) M structure <span class="html-italic">w</span> = 4 mm deformation mode; (<b>b</b>) MM structure <span class="html-italic">w</span> = 7 mm deformation mode; (<b>c</b>) MMG structure <span class="html-italic">w</span> = 7 mm deformation mode; (<b>d</b>) MMLG structure <span class="html-italic">w</span> = 7 mm deformation mode.</p>
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<p>Specific energy absorption and energy absorption proportion of 5 structures.</p>
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26 pages, 11738 KiB  
Article
Active Vibration Control of a Cantilever Beam Structure Using Pure Deep Learning and PID with Deep Learning-Based Tuning
by Abdul-Wahid A. Saif, Ahmed Abdulrahman Mohammed, Fouad AlSunni and Sami El Ferik
Appl. Sci. 2024, 14(24), 11520; https://doi.org/10.3390/app142411520 - 11 Dec 2024
Viewed by 675
Abstract
Vibration is a major problem that can cause structures to wear out prematurely and even fail. Smart structures are a promising solution to this problem because they can be equipped with actuators, sensors, and controllers to reduce or eliminate vibration. The primary objective [...] Read more.
Vibration is a major problem that can cause structures to wear out prematurely and even fail. Smart structures are a promising solution to this problem because they can be equipped with actuators, sensors, and controllers to reduce or eliminate vibration. The primary objective of this paper is to explore and compare two deep learning-based approaches for vibration control in cantilever beams. The first approach involves the direct application of deep learning techniques, specifically multi-layer neural networks and RNNs, to control the beam’s dynamic behavior. The second approach integrates deep learning into the tuning process of a PID controller, optimizing its parameters for improved control performance. To activate the structure, two different input signals are used, an impulse signal at time zero and a random one. Through this comparative analysis, the paper aims to evaluate the effectiveness, strengths, and limitations of each method, offering insights into their potential applications in the field of smart structure control. Full article
(This article belongs to the Section Materials Science and Engineering)
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<p>The Piezoelectric Effect.</p>
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<p>Assumption that the Plane Sections Remain Plane.</p>
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<p>Cantilever Beam with Two PZT Actuators and Sensor.</p>
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<p>Block Diagram of Open Loop System with Low-Pass Filter under Disturbance.</p>
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<p>Genetic Algorithm-Based PID Tuning Process Flowchart.</p>
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<p>Recurrent Neural Network with Long Short-Term Memory.</p>
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<p>Closed Loop System with Deep Learning Controller under Disturbance.</p>
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<p>Voltage Response of PZT Sensor before Vibration Control (under Impulse Disturbance).</p>
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<p>System Control Signal.</p>
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<p>Voltage Response of PZT Sensor after Vibration Control with Deep Learning Controller (under Impulse Disturbance).</p>
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<p>Voltage Response of PZT Sensor in the Cantilever with Deep Learning Controller and without Controller.</p>
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<p>Random Disturbance.</p>
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<p>Voltage Response of PZT Sensor before Vibration Control (under Random Disturbance).</p>
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<p>System Control Signal.</p>
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<p>Voltage Response of PZT Sensor after Vibration Control with Deep Learning Controller (under Random Disturbance).</p>
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<p>Voltage Response of PZT Sensor in the Cantilever Beam with Deep Learning Controller and without Controller.</p>
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<p>Closed Loop System with DL-PID Controller under Disturbance.</p>
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<p>Deep Learning Network.</p>
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<p>Voltage Response of PZT Sensor before Vibration Control (under Impulse Disturbance).</p>
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<p>System Control Signal.</p>
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<p>Voltage Response of PZT Sensor after Vibration Control with DL-PID Controller (under Impulse Disturbance).</p>
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<p>Voltage Response of PZT Sensor in the Cantilever with DL-PID Controller and without.</p>
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<p>Random Disturbance of the System.</p>
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<p>Voltage Response of PZT Sensor before Vibration Control (under Random Disturbance).</p>
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<p>System Control Signal.</p>
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<p>Voltage Response of PZT Sensor after Vibration Control with DL-PID Controller (under Impulse Disturbance).</p>
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<p>Voltage Response of PZT Sensor in the Cantilever with DL-PID Controller and without.</p>
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30 pages, 62820 KiB  
Article
Novel Artificial Neural Network Aided Structural Topology Optimization
by Xiangrui Kong, Yuching Wu, Peng Zhu, Peng Zhi and Qianfan Yang
Appl. Sci. 2024, 14(23), 11416; https://doi.org/10.3390/app142311416 - 8 Dec 2024
Viewed by 604
Abstract
In this paper, novel artificial neural networks are adopted for the topology optimization of full structures at both coarse and fine scales. The novelty of the surrogate-based method is to use neural networks to optimize the relationship from boundary and mesh conditions to [...] Read more.
In this paper, novel artificial neural networks are adopted for the topology optimization of full structures at both coarse and fine scales. The novelty of the surrogate-based method is to use neural networks to optimize the relationship from boundary and mesh conditions to structure density distribution. The objective of this study is to explore the feasibility and effectiveness of deep learning techniques for structural topology optimization. The newly developed neural networks are used for optimizing various types of structures with different meshes, partition numbers, and parameters. The finite element computation takes more than 90% of the total operation time of the SIMP method, but it decreases to 40%. It is indicated that the computational cost for the whole structural design process is relatively low, while the accuracy is acceptable. The proposed artificial neural network method is used to perform topology optimization for some numerical examples such as the cantilever beam, the MBB beam, the L-shape beam, the column, and the rod-supported bridge. It is demonstrated that computational efficiency is considerably improved while the proposed neural network method is adopted. Full article
(This article belongs to the Section Civil Engineering)
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<p>Schematic diagram of partitioned neural network architecture.</p>
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<p>Density, sensitivity, and displacement maps of sample structures at different partitions, (<b>a</b>) 60 × 60, (<b>b</b>) 30 × 30, and (<b>c</b>) 20 × 20.</p>
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<p>Descent of loss function of neural networks with (<b>a</b>) 5 and (<b>b</b>) 10 hidden layers.</p>
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<p>Training loss function descent history.</p>
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<p>(<b>a</b>) Fine-scale structure density map; (<b>b</b>) difference between results from SIMP with and without ANN.</p>
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<p>Boundary conditions and topological configuration of the cantilever beam with 60 × 60 mesh loaded at the middle of the right end.</p>
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<p>Boundary conditions and topological configuration of the MBB beam with 360 × 120 mesh.</p>
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<p>Boundary conditions and topological configuration of the L-shaped beam with 240 × 240 meshes.</p>
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<p>Boundary conditions and topological configuration of the 1/3 column with 240 × 240 meshes.</p>
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<p>Boundary conditions and topological configuration of the 1/3 rod-supported bridge with 240 × 240 mesh.</p>
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<p>The descent history of the objective function for five numerical examples.</p>
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<p>Comparison between iterative objective functions of SIMP and ANN.</p>
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<p>The proportion of time consumption for each module of the SIMP method with (<b>a</b>) 60 × 60, (<b>b</b>) 120 × 120, (<b>c</b>) 240 × 240, and (<b>d</b>) 480 × 480 meshes.</p>
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<p>The proportion of time consumption of each module in the neural network method for 3×3 partitioned structure with (<b>a</b>) 60 × 60, (<b>b</b>) 120 × 120, (<b>c</b>) 240 × 240, and (<b>d</b>) 480 × 480 meshes.</p>
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28 pages, 10431 KiB  
Article
Numerical Assessment of the Hydrodynamic Excitation Characteristics of a Pelton Turbine
by Longgang Sun, Wenrui Fan, Hengte Zhou, Zhaoning Wang and Pengcheng Guo
Sustainability 2024, 16(23), 10667; https://doi.org/10.3390/su162310667 - 5 Dec 2024
Viewed by 581
Abstract
The Pelton turbine is an ideal choice for developing high-head hydropower resources. However, its cantilever-beam structure exposes the runner to intense alternating loads from high-velocity jets, causing localized high stresses, structural vibrations, and potential bucket fractures, all of which compromise safe operation. This [...] Read more.
The Pelton turbine is an ideal choice for developing high-head hydropower resources. However, its cantilever-beam structure exposes the runner to intense alternating loads from high-velocity jets, causing localized high stresses, structural vibrations, and potential bucket fractures, all of which compromise safe operation. This study employs fluid–structure interaction analysis for the numerical investigation of a six-nozzle Pelton turbine to examine its unstable flow characteristics and hydrodynamic excitation under high-velocity jets. Our findings indicate that low-order frequencies primarily induce overall runner oscillations, while high-order frequencies result in oscillation, torsional displacement, and localized vibrations. Torsional displacement at the free end of the bucket induces stress concentrations at the root of the bucket and the splitter, the outflow edge, and the cut-out. The amplitudes of stress and displacement are correlated with the nozzle opening, with displacement typically in phase with torque, while stress fluctuations exhibit a phase lag. The stress and displacement values are higher on the bucket’s front, with maximum stress occurring at the bucket root and maximum displacement at the outflow edge, particularly in regions subjected to prolonged jet impact. The dominant frequency of the stress pulsations matches the number of nozzles. This study elucidates the dynamic response of Pelton turbines under high-velocity jets, correlating fluid load with runner dynamics, identifying maximum stress and deformation points, and providing technical support for performance evaluation. Full article
(This article belongs to the Section Energy Sustainability)
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<p>Three-dimensional geometric structure of the Pelton turbine. (<b>a</b>) the Pelton turbine; (<b>b</b>) the nozzle opening.</p>
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<p>Comprehensive characteristic curve of the Pelton turbine model.</p>
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<p>Boundary condition settings.</p>
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<p>Grid generation of Pelton turbine. (<b>a</b>) water supply mechanism. (<b>b</b>) injector. (<b>c</b>) runner.</p>
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<p>Grid independence verification results.</p>
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<p>Distribution of <span class="html-italic">y</span><sup>+</sup> on nozzle and runner.</p>
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<p>Pelton turbine model test rig and main flow components.</p>
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<p>Torque–time curves of the runner under different opening conditions. (<b>a</b>) total torque of the runner at <span class="html-italic">s</span><sub>0.38</sub>; (<b>b</b>) torque at three operating points.</p>
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<p>Torque of a single bucket and its relative position to the jet. (<b>a</b>) total torque of the runner at <span class="html-italic">s</span><sub>0.38</sub>; (<b>b</b>) position of bucket relative to jet. (<span class="html-italic">α</span><sub>1</sub>–<span class="html-italic">α</span><sub>3</sub>: the jet cuts the bucket; <span class="html-italic">α</span><sub>3</sub>–<span class="html-italic">α</span><sub>5</sub>: the water film fully contacts the bucket; <span class="html-italic">α</span><sub>5</sub>–<span class="html-italic">α</span><sub>1’</sub>: the water film flows out).</p>
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<p>Distribution of water and air on the bucket and turbulent kinetic energy. (<b>a</b>) <span class="html-italic">α</span><sub>2</sub>;(<b>b</b>) <span class="html-italic">α</span><sub>4</sub>; (<b>c</b>) <span class="html-italic">α</span><sub>5</sub>; (<b>d</b>) <span class="html-italic">α</span><sub>6</sub>. (The arrows indicate the positions of the jet on the splitter).</p>
Full article ">Figure 11
<p>First ten mode shapes of the runner under the condition of <span class="html-italic">s</span><sub>0.38</sub>.</p>
Full article ">Figure 12
<p>Discrepancies in natural frequency for each mode.</p>
Full article ">Figure 13
<p>Equivalent stress and displacement of the runner. (<b>a</b>) the positions of injectors; (<b>b</b>) equivalent stress; (<b>c</b>) displacement. (purple arrows are jet, red circles are the bucket in the second row of the figure).</p>
Full article ">Figure 13 Cont.
<p>Equivalent stress and displacement of the runner. (<b>a</b>) the positions of injectors; (<b>b</b>) equivalent stress; (<b>c</b>) displacement. (purple arrows are jet, red circles are the bucket in the second row of the figure).</p>
Full article ">Figure 14
<p>Time-domain information on the runner’s stress and displacement. (<b>a</b>) Maximum equivalent stress; (<b>b</b>) Maximum displacement; (<b>c</b>) Maximum equivalent stress, displacement, and torque at <span class="html-italic">s</span><sub>0.51</sub>; (<b>d</b>) Displacement along x direction; (<b>e</b>) Displacement along y direction.</p>
Full article ">Figure 15
<p>Equivalent stress measurement points on the bucket (A representing the working surface and B representing the outside, and the working surface of the bucket is divided into seven regions. For example, A11 represents the first monitoring point in the region 1 of the working surface).</p>
Full article ">Figure 16
<p>Time- and frequency-domain information on the equivalent stresses at the cutting edge. (<b>a</b>) A11; (<b>b</b>) A13; (<b>c</b>) B13.</p>
Full article ">Figure 16 Cont.
<p>Time- and frequency-domain information on the equivalent stresses at the cutting edge. (<b>a</b>) A11; (<b>b</b>) A13; (<b>c</b>) B13.</p>
Full article ">Figure 17
<p>Time- and frequency-domain information on the equivalent stresses at the splitter. (<b>a</b>) A71; (<b>b</b>) A73; (<b>c</b>) A75.</p>
Full article ">Figure 17 Cont.
<p>Time- and frequency-domain information on the equivalent stresses at the splitter. (<b>a</b>) A71; (<b>b</b>) A73; (<b>c</b>) A75.</p>
Full article ">Figure 18
<p>Time- and frequency-domain information on the equivalent stresses near the outlet edge. (<b>a</b>) A5; (<b>b</b>) A61; (<b>c</b>) A62; (<b>d</b>) A63.</p>
Full article ">Figure 19
<p>Time- and frequency-domain information on the equivalent stresses at the root of the bucket.</p>
Full article ">Figure 20
<p>Displacement monitoring positions on the bucket (a representing the working surface and b representing the outside, and a11 represents the first monitoring point in the first row of the working surface).</p>
Full article ">Figure 21
<p>Displacement inside the bucket in the radial direction. (<b>a</b>) a14; (<b>b</b>) a24; (<b>c</b>) a34.</p>
Full article ">Figure 22
<p>Displacement inside the bucket in the span direction. (<b>a</b>) a11; (<b>b</b>) a12; (<b>c</b>) a13.</p>
Full article ">Figure 23
<p>Displacement on the outside of the bucket in the radial direction. (<b>a</b>) b24; (<b>b</b>) b34.</p>
Full article ">Figure 24
<p>Displacement on the outside of the bucket in the span direction. (<b>a</b>) b21; (<b>b</b>) b22; (<b>c</b>) b23.</p>
Full article ">Figure 25
<p>Displacement of bucket splitter. (<b>a</b>) a21; (<b>b</b>) a31; (<b>c</b>) b31.</p>
Full article ">
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