FR3036558A1 - ELASTIC WAVEGUIDE STRUCTURE FORMED ON A PLATE - Google Patents

Abstract

The invention relates to a resilient wave confinement device comprising: a plate (PL) fixed to a rigid support (SP) at fixed points (FP) distributed on the plate along two lateral lines (LL1, LL2) delimiting between them a confinement region without a fixed point (WG), outside which the fixed points are spaced apart from each other at a maximum distance of a first distance, the two lateral lines being spaced apart from one another by at least one second distance greater than the first distance, and an excitation zone (EP) located on the plate in the confinement region, where elastic waves are applied to the confinement region.

Description

The present invention relates to phononic structures and in particular to devices for driving and / or confining elastic or acoustic waves. BACKGROUND OF THE INVENTION The present invention is applicable to many fields such as including actuators and piezoelectric transducers used to generate or detect acoustic waves, and delay lines. The present invention can also be used to improve the performance of magnetic induction devices and electric motors, as well as the performance of SAW (Surface Acoustic Waves) or bulk acoustic wave (BAW) bulk acoustic wave devices (Bulk Acoustic Waves). . In a homogeneous medium, different types of elastic waves are likely to spread. In general, these waves are polarized either in the direction of propagation (longitudinal waves) or in an orthogonal direction (shear waves). If the medium is semi-infinite, that is to say if it has a free interface and an "infinite" thickness, so-called Rayleigh surface waves can propagate there. In the case where the material constituting the propagation medium is anisotropic any "pseudo surface waves" may appear. The case of the plates is particularly interesting since the elastic waves that can propagate there are confined and completely guided. The waves that can propagate in a plate are Rayleigh surface waves propagating independently on both interfaces of the plate at the same speed. These waves have a small wavelength relative to the thickness of the plate. For a given plate, at longer wavelengths, so-called "bending" and "compression" propagation modes tend to separate, and the difference between the propagation speeds on the two plate interfaces tends to to increase. In A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, Phys. Rev. E 74, 046610 (2006), the possibility of controlling the dispersion of elastic plate waves by structuring thereof has been demonstrated. This structuring is formed by elementary cells distributed on the plate periodically. Each elementary cell is made by inclusion in the plate, the plate and the inclusions being made of different materials. This structuring prohibits the propagation of elastic waves having a wavelength close to twice the distance separating two adjacent inclusions in the direction of propagation of the waves. This phenomenon is a consequence of so-called Bragg interference. Such a structure therefore becomes very cumbersome if one wishes to exploit this phenomenon at long wavelengths. In addition, the bandgap at wavelengths close to twice the distance separating two adjacent inclusions is relatively narrow. In T. T. Wu, Z. G. Huang, T. C. Tsai, T. C. Wu, Appl. Physic Letters 93, 111902 (2008), it has been demonstrated that it is possible to control elastic waves propagating in a plate, by means of a periodic structuring whose elementary cell comprises a resonant cylindrical pillar-shaped inclusion, extending above the plate. The presence of such pillars profoundly changes the distribution of wavelengths that can propagate in the plate. In particular, this structuring allows the opening of banned bands at 20 long wavelengths (large compared to the period of structuring). This principle was subsequently extended and validated experimentally for Rayleigh waves as described in Khelif et al. Phys. Rev. B 81 (21), 214303, 2010, and Achaoui et al. Phys. Rev. B 83 (10), 104201, 2011. It has been shown that a periodic arrangement of pillars makes it possible to control the propagation of these waves on the surface of a semi-infinite medium and that any appearance of forbidden bands local resonance easily resists the random arrangement of these pillars. This made it possible to demonstrate that these forbidden bands depend exclusively on the local resonance of the pillars and not on their periodic distribution (network effect, Achaoui et al J. Appl Phys 114 (10), 104503, 2013). However, as the effect produced by this structuring is based on the resonance of the pillars, the forbidden bands are relatively narrow. It is therefore desirable to provide a confinement device for controlling the propagation of elastic waves in a plate, which is capable of controlling waves having wavelengths in a wide range of wavelengths. that is, large as well as small relative to the thickness of the plate. It is also desirable to increase the efficiency of a waveguide to transmit such elastic waves. Embodiments relate to a method of confining elastic waves in a plate, the method comprising the steps of: securing the plate to a rigid support at fixed points distributed on the plate along two lateral lines delimiting between them a region 10 confinement without a fixed point, outside which the fixed points are spaced apart from each other not more than a first distance, the two lateral lines being spaced from each other at least a second distance greater than the first distance, and apply elastic waves to the plate at an excitation zone in the confinement region. According to one embodiment, in which the distribution of the fixed points outside the confinement region defines a first low cutoff frequency of elastic waves capable of propagating in the plate, below which the elastic waves can not traversing the lateral lines, and the second distance defines a second low cutoff frequency of elastic waves capable of propagating in the confinement region, the second cutoff frequency being lower than the first cutoff frequency. According to one embodiment, the elastic waves applied to the plate in the confinement region have a frequency between the first and second cutoff frequencies. According to one embodiment, the method comprises a step of fixing on the plate in the confinement region resonators each having a resonant frequency lower than the second cutoff frequency. According to one embodiment, the resonators fixed in the confinement region define a third low cutoff frequency of elastic waves that can propagate in the confinement region, below which the elastic waves do not propagate in the region 3036558 4 of confinement, the third cutoff frequency being lower than the second cutoff frequency. According to one embodiment, the elastic waves applied to the plate in the confinement region have a frequency between the second and third cutoff frequencies. Embodiments may also relate to a resilient wave confinement device comprising: a plate attached to a rigid support at fixed points distributed on the plate along two lateral lines delimiting between them a confinement region without a fixed point, outside whereof the fixed points are spaced apart from each other by not more than a first distance, the two lateral lines being spaced from one another at least a second distance greater than the first distance, and a zone of excitation located on the plate in the confinement region, where elastic waves are applied to the confinement region. According to one embodiment, the distribution of the fixed points outside the confinement region defines a first low cutoff frequency below which the elastic waves capable of propagating in the plate can not cross the lateral lines, and the second distance defines a second low cutoff frequency of elastic waves that can propagate in the confinement region, the second cutoff frequency being lower than the first cutoff frequency. According to one embodiment, the elastic waves confined in the confinement region have a frequency between the first and second cutoff frequencies. According to one embodiment, the device comprises resonators attached to the plate in the confinement region each having a resonant frequency lower than the second cutoff frequency.

According to one embodiment, the resonators fixed in the confinement region define a third low cutoff frequency of elastic waves capable of propagating in the confinement region, the third cutoff frequency being lower than the second cutoff frequency.

According to one embodiment, the elastic waves confined in the wave confinement region have a frequency between the second and third cutoff frequencies. According to one embodiment, the fixed points have a periodic distribution on the plate outside the confinement region. According to one embodiment, the confinement region has an opening communicating with a region without fixed point of the plate, and having a width greater than the first distance, so as to form a waveguide in which the elastic waves are susceptible to spread to the area without a fixed point. Exemplary embodiments of the invention will be described in the following, without limitation in connection with the accompanying figures in which: Figure 1 is a top view of a plate forming an elastic waveguide, according to a Embodiment 2 is a cross-sectional view of the plate of FIG. 1, FIGS. 3A, 3B show bands of elastic wave propagating in a plate, respectively without and with a waveguide such as that formed in the plate shown in FIG. 1, FIG. 3B also showing frequency dispersion curves as a function of the normalized wavenumber, FIGS. 4A and 4B show amplitude distribution curves of FIG. waves having a first wavelength, propagating in the plate of FIG. 1, respectively along X and Y axes situated in the plane of the plate, FIG. 5 represents a distribution curve along the X axis, of the am wave wave having a second wavelength, propagating in the plate of FIG. 1; FIG. 6 is a top view of a plate in which a waveguide is formed according to another embodiment FIG. 7 is a cross-sectional view of the plate of FIG. 6; FIG. 8 shows variation curves of the transmission of elastic waves in the plates of FIGS. 1 and 6, as a function of the frequency of the waves. FIG. 9 represents frequency dispersion curves as a function of the normalized wavenumber, of elastic waves propagating in the plate shown in FIG. 6, FIGS. 10 to 12 show distribution curves according to FIG. X-axis, the amplitude of waves having different wavelengths, propagating in the plate of Figure 6. Figures 1 and 2 show a PL plate, according to one embodiment. The plate PL is fixed to a rigid support SP by fixed points FP. The fixed points are distributed periodically, that is, aligned in rows and columns, and spaced at the same distance. The FP fixed points delimit a confinement region without fixed point forming in the example of Figure 1 a WG waveguide of elastic waves. The plate PL is built-in type as it is fixed to a fixed and rigid support and fixed points FP. The waveguide WG is formed by a defect 15 realized by deleting a fixed point array FP. Figures 1 and 2 show a median X axis of the waveguide WG coinciding with the row of fixed points deleted. Figure 1 shows a Y axis perpendicular to the X axis, located in the plane of the plate PL. Figure 2 shows an axis Z perpendicular to the plane of the PL plate.

FIGS. 3A, 3B show graphs of bands of elastic waves propagated in the plate PL shown in FIG. 1, when the plate is infinite (the edge effects have not been taken into account) or surrounded by a device preventing the reflection of waves by the edges. The graph of FIG. 3A was obtained in the presence of all the inclusions (in the absence of the confinement region formed by the deletion of a row of fixed points), and thus without any defects. The graph of FIG. 3A shows that the plate PL has forbidden bands FBG1, FBG2 in which no elastic wave propagates. The bandgap FBG1 extends at all frequencies below a low cutoff frequency CF0 of about 74 kHz. The bandgap FBG2 extends at frequencies between about 90 and 110 kHz. In an NBG band extending between the cutoff frequency CF0 and about 90 kHz, the elastic waves propagate throughout the PL plate. The graph of FIG. 3B was obtained from the plate PL of FIG. 1 in the presence of the waveguide WG, by applying elastic waves from an excitation point EP located in the guide. WG wave. The graph of FIG. 3B shows forbidden bands FBG3, FBG4 in which no elastic wave propagates. The band gap FBG3 extends at frequencies below a low cutoff frequency CF1 of about 24 kHz. The band gap FBG4 extends at frequencies between about 57 and 63 kHz. The band NGB extending between the cutoff frequency CF0 and about 90 kHz in which the elastic waves propagate throughout the PL plate remains. As a result, in the NGB band, the elastic waves are not guided in the waveguide WG. FIG. 3B also shows frequency dispersion curves C1, C2, C3 as a function of the normalized wavenumber. The dispersion curve C1 is located between the forbidden bands FBG3 and FBG4, and the dispersion curves C2, C3 lie between the bands FBG4 and NBG.

At the frequencies between the cut-off frequencies CF0 and CF1, corresponding to a point of the curves C1, C2, C3 (outside the forbidden band FBG4), the elastic waves can only propagate in the waveguide WG. They are therefore confined and guided in the waveguide WG. The slope at a point considered of the curves C1, C2, C3 corresponds to the speed of propagation of the elastic waves at the frequency corresponding to the point in question. FIGS. 4A and 4B show variation curves of the elastic wave amplitude at 32 kHz applied to the PL plate in the waveguide WG at an excitation point EP, respectively along the X and Y axes. At this frequency, it is between the forbidden bands FBG3 and FBG4. According to FIG. 4B, the waves propagating in the plate PL are perfectly channelized by the waveguide WG, no wave being detected outside the lateral lines LL1, LL2 of fixed points FP delimiting the waveguide . In FIG. 4A, the channelized waves in the waveguide WG have an amplitude forming ripples from the excitation point EP. At the outputs of the waveguide WG, in regions without a fixed point, the amplitude of the waves decreases to disappear, reflecting the dispersion of the waves throughout the width of the PL plate. FIG. 5 shows a variation curve of the elastic wave amplitude at 18 kHz applied to the PL plate in the waveguide WG, along the X axis of the waveguide WG. The excitation point EP is at the entrance of the waveguide WG. At this frequency, we are in the forbidden band FBG3. From FIG. 5, no wave enters the WG guide, the waves applied at the excitation point EP being dispersed throughout the region of the PL without a fixed point. The shape and in particular the width of the waveguide WG (between the fixed points FP), therefore makes it possible to confine and channel elastic waves at relatively low frequencies (between 24 and 74 kHz), located in the forbidden band FBG1 a recessed fixed point plate 10 periodical flawless. Figures 6 and 7 show the PL plate in which is formed a waveguide WG '. As before, the embedded type plate PL comprises fixed points FP for fixing the plate PL to a rigid support SP, the fixed points being distributed periodically, ie aligned in rows and columns and spaced from the same distance. The waveguide WG 'is formed as before, by a defect realized by removing a row of fixed points FP. According to one embodiment, the waveguide WG 'comprises RS resonators fixed on the plate PL (for example at the locations of the fixed points removed), and aligned along the X axis of the waveguide. RS resonators have a shape, a height above the plate, an elasticity and a density, giving them a resonance frequency of their own. In the example of FIGS. 6 and 7, the RS resonators have a cylindrical shape.

FIG. 8 represents curves C11, C12 of variation of the transmission T of elastic waves in the waveguides WG and WG 'of FIGS. 1 and 6, as a function of the frequency F of the elastic waves. The curve C11, corresponding to the waveguide WG formed in the plate PL of FIG. 1, shows that the transmission of elastic waves at frequencies below 80 kHz hardly exceeds 0 dB. Between 0 and 25 kHz, this transmission remains below -40 dB, revealing the presence of the bandgap FBG1. Between 25 and 40 kHz, this transmission has peaks of up to +10 dB. Between 40 and 80 kHz, the transmission of elastic waves remains confined between 0 and -40 dB.

The curve C12 was obtained when the resonators RS have a resonance frequency lower than the low cutoff frequency CF1 of the band FBG3. According to curve C12, the transmission of elastic waves in the waveguide WG 'of FIG. 6 can reach +20dB on average between about 7 and 10 kHz. Between 10 and 15 kHz, the transmission in the waveguide WG 'remains close to 0 dB. Between 15 and 25 kHz, waveguide transmission WG 'has peaks of +15 to +25 dB. Beyond 25 kHz, the transmission of the waveguide WG 'hardly exceeds 0 dB, with peaks lower than -40 dB between 25 and 40 kHz and between 65 and 80 kHz. FIG. 9 represents dispersion curves of the frequency as a function of the normalized wavenumber, of elastic waves propagating in the waveguide WG 'shown in FIG. 6, when the PL plate is infinite (the effects edge of the plate have not been taken into account) or surrounded by a device preventing the reflection of waves by the edges of the plate PL. The graph of FIG. 9 shows that the forbidden bands FBG3 and FBG4 (FIG. 3B) are replaced by forbidden bands FBG5, FBG6 in which no elastic wave propagates. The bandgap FBG5 extends at frequencies below a CF2 low cutoff frequency of about 7 kHz. The band gap FBG6 extends between CF1 frequencies at about 24 kHz and about 39 kHz. The band gap FBG6 corresponds to the attenuation observed in this band in FIG. 8. The band NGB extending between the frequencies CF0 and approximately 90 kHz is still present. As a result, in the NGB band, the elastic waves 25 are not guided in the waveguide WG '. Figure 9 also shows dispersion curves C4, C5, C6 between the forbidden bands FBG5 and FBG6, and dispersion curves C7, C8, C9 between the bands FBG6 and NBG. At the frequencies corresponding to a point of the curves C4 to C9, the elastic waves are guided in the waveguide WG '. The slope at a considered point of the curves C4 to C9 corresponds to the speed of propagation of the elastic waves at the frequency corresponding to the point considered. As a result, the introduction into the waveguide WG 'of the resonators RS having a resonance frequency between the cut-off frequencies CF1 and CF2, allows the confinement and the propagation of elastic waves with larger wavelengths only in the waveguide WG. It can also be observed that the curves C4, C5 located at the lowest frequencies (between 7 and 11 kHz approximately) have a slight slope. A phenomenon of energy accumulation can therefore be observed at these frequencies. This phenomenon can produce an exaltation of the wave at the output of the resonator guide WG '. Figures 10, 11 and 12 show X-axis variation curves of the amplitude of elastic waves applied to the PL plate in the waveguide WG 'at an excitation point EP, when the frequency The excitation of the PL plate lies respectively in the forbidden band FBG6 (for example 32 kHz), and between the forbidden bands FBG5 and FBG6 at about 18 kHz and 7.5 kHz. In FIG. 10, the excitation point EP is at the input of the waveguide WG 'and the resonators RS are placed from this input. The excitation frequency of the PL plate is located in the forbidden band FBG6 (for example 32 kHz). According to the curve of FIG. 10, no wave penetrates the guide WG ', the waves applied to the excitation point EP being dispersed throughout the region of the plate PL without a fixed point FP outside the waveguide WG.

In FIG. 11, the excitation point EP is in the waveguide WG ', close to a first of the RS resonators. The excitation frequency of the plate PL is about 18 kHz, that is to say on the curve C6 between the bandgap FBG5 and FBG6. The curve of FIG. 11 shows that the amplitude of the guided waves in the guide WG 'forms ripples in the portion of the waveguide comprising the RS resonators. The maximum value of the amplitude of these undulations slightly exceeds the excitation amplitude of the PL plate. At the output of the waveguide WG ', the waves have substantially the same amplitude as that of the waves at the excitation point EP. Outside the waveguide WG ', in the region of the plate without a fixed point, the waves disperse and thus their amplitude drops rapidly. In FIG. 12, the excitation point EP is at the input of the waveguide WG ', close to a first of the resonators RS. The excitation frequency of the PL plate is about 7.5 kHz, on the C4 curve between the 35 forbidden bands FBG5 and FBG6. The curve of FIG. 12 shows two 6-unit peaks and a 2-unit trough for a 2-unit excitation amplitude in the waveguide region WG 'equipped with RS resonators, which represents a multiplication of the amplitude by 3, revealing a phenomenon of accumulation of energy or exaltation. It can also be observed that the amplitude of the waves at the output of the waveguide WG 'is greater than (of the order of two times) that of the waves at the excitation point EP at the input of the waveguide. 'wave. This phenomenon of exaltation can also be observed on the curve C12 (FIG. 8) where, between 7 and 10 kHz, the transmission T can reach +20 dB on average. Outside the waveguide WG ', in the region of the plate without fixed point, the waves disperse and thus their amplitude drops rapidly. This phenomenon of excitement can be usefully exploited to, for example, transmit vibrations to a piezoelectric device. This device makes it possible to obtain a ratio between the amplitude of the vibrations in the excitation zone of the plate and the amplitude of the electrical signal produced by the piezoelectric device, which is significantly higher than in the absence of the RS resonators. . It will be apparent to those skilled in the art that the present invention is capable of various alternative embodiments and various applications.

In particular, the invention is not limited to a plate embedded by fixed points having a periodic distribution. Indeed, this distribution can be random. It is simply important that the fixed points outside the confinement region are spaced from each other by a distance less than a maximum distance depending on the frequencies being processed. Thus, the distance between the fixed points delimiting the waveguide zone can be zero, so as to form fixed continuous lines. In order to form the waveguide WG or WG ', it is simply important that the width of the waveguide be greater than the maximum distance between the fixed points of the plate outside the waveguide. On the other hand, it can be observed that as the width of the waveguide increases from the distance between the fixed points delimiting the waveguide, the more the cutoff frequency CF1 decreases from the cutoff frequency CFO, to become zero. The lateral lines LL1, LL2 of fixed points FP delimiting the waveguide WG, WG 'are not necessarily straight or parallel. The 3036558 12 low cutoff frequency CF1 of the waveguide is then defined by the minimum distance between lines LL1, LL2. The invention is also not limited to a waveguide with openings at its ends. It is simply important that the FP 5 fixed points delimit a confinement region wider than the maximum distance between the fixed points. In addition, a waveguide can be obtained simply from a confinement zone surrounded by fixed points spaced a maximum distance smaller than the width of the confinement zone, by placing an excitation zone and a zone capturing elastic waves 10 in the confinement region. Indeed, the confinement region then forms a waveguide between the excitation zone and the capture zone, for elastic waves having a frequency comprised between the low cutoff frequency of the regions of the plate embedded by the fixed points. and the low cutoff frequency of the confinement region. Thus, for example, a piezoelectric device 15 can be attached to the capture area. The plate may also be formed of a piezoelectric material, electrodes being fixed opposite one another on both sides of the plate in the capture zone. The wavelengths of elastic waves propagating in the plate and confined in the waveguide are not necessarily large relative to the thickness of the plate. Thus, these elastic waves may be surface waves (Raleigh) when their wavelength is close to or less than the thickness of the plate PL. In this regard, it should be pointed out that the frequency values shown in FIGS. 3A, 3B, 8 and 9 are only given by way of example. In fact, these frequency values depend on the distances between the fixed points FP of embedding of the plate PL, and vary in a manner inversely proportional to these distances. Thus, to channel elastic waves having a frequency ten times higher, for example, it is sufficient to reduce the distance between the fixed points of a ratio of ten.

Claims (14)

REVENDICATIONS1. A method of confining elastic waves in a plate (PL), the method comprising the steps of: securing the plate to a rigid support (SP) at fixed points (FP) distributed on the plate along two lateral lines (LL1, LL2) delimiting between them a confinement region (WG, WG ') without a fixed point, outside which the fixed points are spaced from each other at most a first distance, the two lateral lines being spaced apart at the other at least a second distance greater than the first distance, and apply elastic waves to the plate at an excitation zone (EP) in the confinement region. 2. Method according to claim 1, in which the distribution of the fixed points (FP) outside the confinement region (WG, WG ') defines a first low cutoff frequency (CFO) of elastic waves 15 likely to propagate. in the plate (PL), below which the elastic waves can not cross the lateral lines (LL1, LL2), and the second distance defines a second low cutoff frequency (CF1) of elastic waves likely to propagate in the the confinement region, the second cutoff frequency being less than the first cutoff frequency. The method of claim 2, wherein the elastic waves applied to the plate in the confinement region (WG) have a frequency between the first and second cutoff frequencies (CFO, CF1). 4. Method according to one of claims 2 and 3, comprising a step of fixing on the plate (PL) in the confinement region (WG ') of resonators (RS) each having a resonant frequency lower than the second frequency cutoff (CF1). 5. Method according to one of claims 2 to 4, wherein the resonators (RS) fixed in the confinement region (WG ') define a third low cutoff frequency (CF2) elastic waves likely to spread in the confinement region, below which the elastic waves do not propagate in the confinement region, the third cutoff frequency being lower than the second cutoff frequency (CF1). 6. The method of claim 5, wherein the elastic waves applied to the plate in the confinement region (WG ') have a frequency between the second and third cutoff frequencies (CF1, CF2). 7. Apparatus for confining elastic waves comprising: a plate (PL) fixed to a rigid support (SP) at fixed points (FP) distributed on the plate along two lateral lines (LL1, LL2) delimiting between them a region confinement without a fixed point (WG, WG '), outside which the fixed points are spaced from each other at a maximum distance of a first distance, the two lateral lines being spaced apart from each other at a minimum of a second distance greater than the first distance, and an excitation zone (EP) located on the plate in the confinement region, where elastic waves are applied to the confinement region. 8. A device according to claim 7, wherein the distribution of the fixed points (FP) outside the confinement region (WG, WG ') defines a first low cutoff frequency (CFO) below which the elastic waves are susceptible. to propagate in the plate can not cross the lateral lines (LL1, LL2), and the second distance defines a second low cutoff frequency (CF1) of elastic waves likely to propagate in the confinement region, the second frequency 30 cutoff being less than the first cutoff frequency. 9. Device according to claim 8, wherein the elastic waves confined in the confinement region have a frequency between the first and second cutoff frequencies (CFO, CF1). 35 3036558 10. Device according to claim 7 or 8, comprising resonators (RS) fixed to the plate (PL) in the confinement region (WG ') each having a resonant frequency lower than the second cutoff frequency (CF1). 5 11. Device according to claim 10, wherein the resonators (RS) fixed in the confinement region (WG ') define a third low cutoff frequency (CF2) of elastic waves capable of propagating in the confinement region, the third cutoff frequency 10 being less than the second cutoff frequency (CF1). 12. Device according to claim 11, wherein the elastic waves confined in the wave confinement region have a frequency between the second and third cut-off frequencies (CF1, CF2). 13. Device according to one of claims 7 to 12, wherein the fixed points (FP) have a periodic distribution on the plate (PL) outside the confinement region (WG, WG '). 14. Device according to one of claims 7 to 13, wherein the confinement region (WG, WG ') has an opening communicating with a region without fixed point of the plate (PL), and having a width greater than the first distance, so as to form a waveguide in which the elastic waves are likely to propagate to the region without fixed point.