Holding device for piezoelectric resonator and power converter comprising it

Abstract

Title: Holding device for piezoelectric resonator and power converter comprising it The invention relates to the field of power converters, and more particularly to the field of holding devices for piezoelectric resonators, in particular intended to be used as an inductive component within power converters. The invention, according to its various aspects, proposes a new holding device for a piezoelectric resonator making it possible to minimize the deformation energy transmitted to it by the resonator in operation, while allowing the electrical connections to be resumed at the electrodes of the resonator.In addition, the proposed holding device tends to reduce the overall system size, i.e., the resonator in its holding device, which is a crucial issue for the desired volume reduction, especially when the holding device and the resonator form at least part of a power converter. Figure for abstract: Fig. 4.

Description

Title of the invention: Holding device for piezoelectric resonator and power converter comprising it Technical field

[0001] The present invention relates to the field of power converters, and more particularly to the field of holding devices for piezoelectric resonators, in particular intended to be used as an inductive component within power converters. STATE OF THE ART

[0002] Power converters are now ubiquitous in our daily lives, enabling us to power all of our electronic devices, whether portable or not. We are always looking to make them both smaller and less lossy.

[0003] To do this, one of the proposed solutions is to increase their operating frequency in order to reduce the volume of the transient energy storage components (i.e. the passive ones). However, there are still limits to this increase in frequency. They are observed in particular on the side of magnetic storage components which have intrinsic iron losses and are subject to the skin effect phenomenon; both phenomena worsen when the frequency increases. This is detrimental to improving the efficiency of power converters.

[0004] In order to overcome these limits, the use of piezoelectric resonators has been proposed. These resonators are used, for the purpose of constituting power converters, between their resonance frequency and their antiresonance frequency on a natural mode of their structure (for example transverse (radial), longitudinal, etc.). Between these two frequencies, they have characteristics similar to those of the magnetic inductances that we seek to replace. The resonance modes used are of a mechanical nature. Thus, the impact of the resonator holding device must be taken into account because it can be the cause of wave leaks (therefore losses), but also of the appearance of new resonance modes that can interfere with the system in its operating band.It is then crucial to find a system that ensures both correct mechanical support of the piezoelectric resonator and also allows a good electrical connection necessary for the use of the piezoelectric resonator.

[0005] Today, piezoelectric resonators are found in the automobile industry for fuel injection, water sprayers, ultrasonic cleaning, precision positioning, plasma generators, but also in the world of telecommunications for the production of radiofrequency filters. In this last use case, resonators are regularly required to work on the whole band located between their resonance frequency and their antiresonance frequency on a selected resonance mode, which is less the case for other applications. This is why the state of the art discussed below is devoted to solutions developed for the production of radiofrequency filters.

[0006] For example, it is known from the patent document referenced EP1041714 A2, a device for holding a piezoelectric resonator operating in a longitudinal mode. The holding is achieved by means of a mechanical junction made of a material (referenced 40 in [Fig. 4] of the patent document EP1041714 A2) having an acoustic impedance significantly different from that of the resonator. In addition, anchoring points (referenced 40a in [Fig. 4] of the patent document EP1041714 A2), between the resonator and the holding device, are located approximately in line with the center of the resonator. Physically, these anchoring points correspond to the points where the material displacements are almost zero, but where the stress is maximum for the longitudinal mode which is addressed by this patent.

[0007] This technical solution is interesting, because it allows the acoustic foundation to be confined without the need to dimension any elements; it is simply sufficient to produce the proposed central mechanical junction in a conductive material having acoustic properties different from those of the fixed resonator. Thus, the deformation foundation, of low amplitude because it is in the center of the material, is reflected largely between, on the one hand, the resonator and the substrate (referenced 12 in [Fig.4] of patent document EP1041714 A2) and, on the other hand, the material constituting the mechanical junction.

[0008] However, the mechanical junction between the resonator and its support is punctual. In fact, the mechanical resistance of the assembly is poor and this type of solution is applicable to small resonators with a low mass.

[0009] In the case of power conversion, we want to be able to use massive resonators in order to store a maximum amount of energy within them (which depends on the volume of material used). This type of support therefore does not appear to be robust enough. In addition, in certain applications, a purely planar integration could be desired, which is not possible with the type of mechanical junction disclosed in patent document EP1041714 A2. It is also necessary to find an additional means of electrical connection to access the higher potential of the piezoelectric resonator.

[0010] Also known from the patent document referenced CN109546986 is a piezoelectric resonator support for microelectromechanical systems, hereinafter MEMS, used in radio frequency. The support is such that it implements very low stiffness attachment structures to hold the piezoelectric resonator. In order to minimize the energy transmitted to the support, the piezoelectric resonator, in position central, operates in such a way that it exhibits nodes at its anchor points on the support.

[0011] This solution is used when the dimension of the flexible elements of the support becomes too small to be machined directly in the form of straight bars (which is the case for very high frequency resonators). By proposing specific shapes for these flexible elements, their holding stiffness is reduced and the energy transmitted by the resonator to the support is also reduced.

[0012] However, it is noted that the proposed support uses a very large surface area which is not desired, in particular for power conversion. In addition, in order to be efficient and to minimize losses, the support requires the generation of nodes at the periphery of the piezoelectric resonator. Consequently, as the resonator does not work in a first mode, it loses its ability to exchange energy, which is not advantageous when one wishes to develop a solution whose main application consists of power conversion.

[0013] Another solution, aimed at minimizing the holding losses of a piezoelectric resonator in the case of the production of MEMS used in radiofrequency, is described in the scientific article by BP Harrington et al., entitled "In-plane acoustic reflectors for reducing effective anchor loss in lateral-extensional MEMS resonators", and published in J. Micromech. Microeng. 21 (2011) 085021. In order to confine the deformation wave produced by the piezoelectric resonator, a resonator holding device is proposed which comprises arc-shaped trenches made on its holding edges. These trenches have characteristic dimensions close to the half-wavelength of the excitation deformation, so as to form a reflector to confine the deformation wave.In doing so, at the first holding point with the resonator, a quasi-node is generated; then, when the wave propagates towards the reflector, the majority of it is returned to the fixing point with the resonator. During its reflection, the wave is out of phase by 77 (or 180°). If the characteristic size is such that the reflected wave forms a displacement node on the edge of the reflector, the reflected wave is returned in phase with the first; thus, the reflector ends up accompanying the resonator in its deformation which minimizes the losses due to the holding of the resonator.

[0014] Finally, the area where the acoustic reflector is connected to the rest of the frame constitutes a place where wave leaks continue to disperse. The benefits of the reflector are still considerable, with, according to the authors, a gain of 560% on the mechanical quality factor of the assembly consisting of the resonator and its support.

[0015] This holding device is interesting because it is more compact than that described in the patent document referenced CN109546986, and this due to its holding recovery on the side. However, it is noted that the total surface area necessary for holding remains very important with an occupation close to 1.5 times the surface of the resonator used. Finally, since the piezoelectric substrate must not be excited on the parts outside the resonator, it is necessary to have upper (top) and lower (bottom) electrodes which do not overlap on the fixing parts, which reduces the width of the electrical connection plane to the resonator which, in the case of use for power conversion, needs to be maximized in order to reduce the electrical impedances of connections (both resistive and inductive). Also, the holding device according to BP Harrington et al. assumes zero displacement nodes on the periphery of the resonator to minimize the energy transmitted to the support.

[0016] There therefore remains a need in terms of robust mechanical holding means for the resonator which allow the resonator to vibrate without introducing losses and / or parasitic modes, in particular between its resonance frequency and its antiresonance frequency, on the selected vibration mode.

[0017] More particularly, an object of the present invention is to develop a holding device for a piezoelectric resonator adapted to the constraints induced by the application or applications targeted, including in particular power conversion. SUMMARY

[0018] To achieve this objective, according to a first aspect of the invention, a holding device for a piezoelectric resonator is provided, the holding device comprising at least two elementary cells intended to be mechanically linked together and to be distributed over an inner or outer periphery of the piezoelectric resonator, at least one, preferably each, elementary cell comprising four bars including: • a so-called primary bar by which the holding device is intended to be mechanically linked to the piezoelectric resonator, • two so-called secondary bars, including: i. a first secondary bar: 1. mechanically linked to the primary bar of the elementary cell considered, 2. mechanically linked to an elementary cell adjacent to the elementary cell considered, and 3. intended to be mechanically linked to an external frame, and ii. a second secondary bar: 1. mechanically linked to the primary bar of the elementary cell considered, 2. mechanically linked to an elementary cell adjacent to the elementary cell considered, and 3. intended to be mechanically linked to the external frame, and iii. a so-called tertiary bar mechanically linking the first one together secondary bar and the second secondary bar of the elementary cell considered.

[0019] According to a second aspect of the invention, an assembly is provided comprising a holding device as introduced above and at least one piezoelectric resonator.

[0020] According to a third aspect of the invention, a power converter is provided comprising an assembly as introduced above.

[0021] According to a fourth aspect of the invention, a method is provided for dimensioning a holding device as introduced above, comprising: a. dimensioning at least one, preferably each, primary bar of at least one, preferably each, elementary cell so that, with a piezoelectric resonator configured to vibrate in a determined frequency band, the primary bar is in resonance, to within 20%, advantageously to within 10%, with the vibrations of the piezoelectric resonator for any excitation frequency located in said determined frequency band, and / or b. dimensioning at least one, preferably each, of the first and second secondary bars of at least one, preferably each, elementary cell so that it has a length substantially equal to a multiple of half a wavelength for a chosen excitation frequency located in the determined frequency band, and preferably at its center, or its geometric center, and have, with respect to their longitudinal axis, a quadratic moment at least four times greater, preferably at least ten times greater, than a quadratic moment of the primary bar with respect to its longitudinal axis, and / or c. dimensioning the tertiary bar of at least one, preferably of each, elementary cell, so that it has a length substantially equal to the length of the primary bar of the elementary cell considered, a thickness greater, preferably at least twice greater, than a thickness of the primary bar of the elementary cell considered, and is advantageously adapted in mechanical impedance with the first and second secondary bars of the elementary cell considered.

[0022] Thus, the invention according to its various aspects proposes a new holding device for a piezoelectric resonator making it possible to minimize the deformation energy transmitted to it by the resonator in operation, while allowing the electrical connections to be resumed at the electrodes of the resonator. In addition, the proposed holding device tends to reduce the size of the total system, i.e. of the resonator in its holding device, which is a crucial issue for the desired volume reduction, in particular when the holding device and the resonator form at least part of a power converter. BRIEF DESCRIPTION OF THE FIGURES

[0023] The aims, objects, as well as the characteristics and advantages of the invention will emerge more clearly from the detailed description of an embodiment thereof which is illustrated by the following accompanying drawings in which:

[0024] [Fig.l] [Fig.l] schematically represents a sectional view of an embodiment of an elementary cell of a holding device according to the first aspect of the invention and a part of the piezoelectric resonator that the cell equips.

[0025] [Fig.lA] [Fig.lA] represents an enlargement of the part of [Fig.l] which is framed by a long-short dashed line.

[0026] [Fig.2] [Fig.2] schematically represents a partial sectional view of an embodiment of the holding device according to the first aspect of the invention and a part of the piezoelectric resonator with which the holding device is equipped.

[0027] [Fig.3] [Fig.3] schematically represents the partial sectional view of an embodiment of the holding device according to the first aspect of the invention which is illustrated in [Fig.2] and adds graphic illustrations intended essentially to show how transverse waves propagate in the propagation medium constituted by the holding device.

[0028] [Fig.4] [Fig.4] schematically represents a top view of a piezoelectric resonator taking the form of a disc and of an embodiment of the holding device according to the first aspect of the invention which equips said piezoelectric resonator.

[0029] [Fig.5] [Fig.5] schematically represents a top view of a set of square-shaped piezoelectric resonators and a set of holding devices according to the first aspect of the invention which allow matrixing of said set of piezoelectric resonators.

[0030] The drawings are given as examples and are not limiting of the invention. They constitute schematic representations of principle intended to facilitate the understanding of the invention and are not necessarily on the scale of practical applications. In particular, the relative thicknesses of the different constituent elements of the invention according to its first aspect are not necessarily representative of reality. DETAILED DESCRIPTION

[0031] Before commencing a detailed review of embodiments of the invention, are set out below are optional features that may be used in combination or alternatively:

[0032] According to an example of the first aspect of the invention, at least one, preferably each, primary bar of at least one, preferably each, elementary cell is of dimensions such that, with a piezoelectric resonator configured to vibrate in a determined frequency band, the primary bar is in resonance, to within 20%, advantageously to within 10%, with the vibrations of the piezoelectric resonator for any excitation frequency located in said determined frequency band. That the primary bar is in resonance to within 20%, advantageously to within 10%, with the vibrations of the piezoelectric resonator means that a frequency shift is allowed between the natural frequency of the primary bar at the point of attachment with the piezoelectric resonator if the piezoelectric resonator were not attached and the vibration frequency of the piezoelectric resonator which can be any in the determined frequency band.According to the previous example, the determined frequency band is substantially comprised at most between a resonance frequency and an antiresonance frequency of the piezoelectric resonator on a selected resonance mode.

[0033] According to an example of the first aspect of the invention, at least one, preferably each, of the first and second secondary bars of at least one, preferably each, elementary cell is of dimensions such that it has a length substantially equal to a multiple of half a wavelength for a chosen excitation frequency located in the determined frequency band, and preferably at its center or at its geometric center, and have, with respect to their longitudinal axis, a quadratic moment at least four times greater, preferably at least ten times greater, than a quadratic moment of the primary bar with respect to its longitudinal axis.

[0034] According to an example of the first aspect of the invention, the tertiary bar of at least one, preferably of each, elementary cell, is of dimensions such that it has a length substantially equal to the length of the primary bar of the elementary cell considered, a thickness greater, preferably at least twice greater, than a thickness of the primary bar of the elementary cell considered, and is advantageously matched in mechanical impedance with the first and second secondary bars of the elementary cell considered.

[0035] According to an example of the first aspect of the invention, the elementary cell to which the first secondary bar of the cell in question is mechanically linked is different from that to which the second secondary bar of the cell in question is mechanically linked; the holding device then comprises at least three elementary cells.

[0036] According to an example of the first aspect of the invention, said at least two elementary cells are intended to be distributed around the periphery of the piezoelectric resonator, forming a structure closed on itself, the elementary cell which is mechanically linked to the first secondary bar of the elementary cell considered, is adjacent, in said closed structure, to the elementary cell considered, and the elementary cell which is mechanically linked to the second secondary bar of the elementary cell considered, is adjacent, in said closed structure, to the elementary cell considered, the elementary cells mechanically linked to the elementary cell considered being able to be different from each other.

[0037] According to an example of the first aspect of the invention, the primary bar is dimensioned so as to resonate in a first mode, for example transverse or longitudinal, to within 20%, advantageously to within 10%, for said frequency located in the determined frequency band. The holding device is thus better suited to use of the resonator as a power converter.

[0038] According to an example of the first aspect of the invention, at least one bar, preferably each bar, among the four bars is made from at least one material, preferably isotropic, chosen from: a. a metal, such as brass or copper, b. plastic, c. a ceramic, d. a glass fiber reinforced epoxy resin composite, such as FR-4, and e. a crystal.

[0039] According to an example of the first aspect of the invention, alternative to the previous one, at least one bar, preferably each bar, among the four bars comprises an insulating material and one or more thin metal layers separated by the insulating material, for example a printed circuit board. The holding device according to this example benefits from the fact that a printed circuit board is inexpensive and / or from the fact that the use of a printed circuit board to manufacture the holding device according to the first aspect of the invention makes it possible to use the thin metal layers, where appropriate machined, to easily allow functional electrical contact recovery, in particular to control the operation of the piezoelectric resonator.

[0040] According to an example of the first aspect of the invention, alternative to the two previous ones, at least one bar, preferably each bar, is made from the same piezoelectric material, preferably transverse isotropic, as that in which the piezoelectric resonator is intended to be made. The holding device according to this example may advantageously constitute only a single part or a part in one piece with the electric resonator.

[0041] According to an example of the first aspect of the invention, the primary bar is intended to be mechanically linked to the piezoelectric resonator at a first connection point located substantially between a first end and a second end of the primary bar.

[0042] According to an example of the first aspect of the invention, the primary bar is intended to be mechanically linked to the piezoelectric resonator by means of a lug, the mass of the lug being taken into account where appropriate for the dimensioning of the primary bar.

[0043] According to another example of the first aspect of the invention, the primary bar has a symmetry with respect to an axis normal to the periphery of the resonator around the attachment point.

[0044] According to an example of the first aspect of the invention a. the first secondary bar of the elementary cell considered is mechanically linked by a first of its two ends to the first end of the primary bar of the elementary cell considered, is mechanically linked by a second of its two ends at the same time to a second end of the secondary bar of an elementary cell which, among said at least two elementary cells, is adjacent to the elementary cell considered, and is intended to be mechanically linked to the external frame, and b. the second secondary bar of the elementary cell considered is mechanically linked by a first of its two ends to the second end of the primary bar of the elementary cell considered, is mechanically linked by a second of its two ends at the same time to a second end of the first secondary bar of an elementary cell which, among said at least two elementary cells, is adjacent to the elementary cell considered, and intended to be mechanically linked to the external frame.

[0045] According to an example of the first aspect of the invention, the tertiary bar of the elementary cell considered mechanically connects together the first end of the first secondary bar of the elementary cell considered and the first end of the second secondary bar of the elementary cell considered.

[0046] According to an example of the first aspect of the invention, the tertiary bar of each elementary cell is located in line with and at a distance from the primary bar of the elementary cell considered, and is intended to be located, relative to the outer or inner periphery of the piezoelectric resonator which it contributes to maintaining, at a greater distance than the primary bar of the elementary cell considered.

[0047] According to an example of the first aspect of the invention, said at least two elementary cells are distributed around the periphery of the piezoelectric resonator so that the latter, when operating, exerts an excitation of the same amplitude to within 20%, of preferably to within 10%, and / or of the same phase, to within 30°, preferably to within 15°.

[0048] According to an example of the first aspect of the invention, each primary bar has a thickness at least 10 times greater than the amplitude of deformation that it undergoes due to the operation of the piezoelectric resonator.

[0049] According to an example of the second aspect of the invention, the piezoelectric resonator of the assembly is made from PZT.

[0050] According to another example of the second aspect of the invention, the piezoelectric resonator of the assembly is made from LNO (Lithium Niobiate).

[0051] According to an example of the third aspect of the invention, the piezoelectric resonator is configured to vibrate in at least one of its first vibration modes, for example its transverse vibration mode and / or its longitudinal vibration mode.

[0052] According to an example of the third aspect of the invention, the piezoelectric resonator has a resonance frequency and an antiresonance frequency, different from each other, and is configured to operate between its resonance frequency and its antiresonance frequency.

[0053] An element based on a material A is understood to mean an element comprising this material A and possibly other materials.

[0054] A parameter “substantially equal / greater / less than” a given value means that this parameter is equal / greater / less than the given value, plus or minus 20%, or even 10%, close to this value. A parameter “substantially between” two given values ​​means that this parameter is at least equal to the smallest given value, plus or minus 20%, or even 10%, close to this value, and at most equal to the largest given value, plus or minus 20%, or even 10%, close to this value.

[0055] A mechanical connection between two elements or bars is understood to mean that these two elements or bars contact each other without mechanical play at at least one point or zone of connection or contact. Preferably, two elements or bars mechanically connected to each other contact each other directly; in which case, we can speak of a direct mechanical connection, or of elements or bars directly mechanically connected to each other. In this way, mechanical stresses, in particular linked to a displacement of at least one of the two elements or bars mechanically connected to each other, propagate to the other element or bar, this propagation of mechanical stresses depending, in particular on their nature and their amplitude, on the designs (at least shape and dimensions) of the elements or bars concerned.

[0056] By operating nodes is meant remarkable zones of the holding device according to the first aspect of the invention, which are not necessarily punctual, but which can on the contrary be extended, their extension however remaining of small dimensions, for example ten times smaller, relative to the di dimensions of the bars. The operating nodes of the holding device according to the first aspect of the invention are for example located in the zones which, in [Fig.4], are delimited by the oval curves in bold dashes, each of these zones comprising an operating node.

[0057] With reference to Figures 1 and 1A, one of the objectives pursued by the present invention consists in providing a holding device 1 (sometimes called below "fixing") of a piezoelectric resonator 2 on an external frame (or package) 3 which is adapted to the constraints induced by certain applications, and in particular power conversion. The holding device 1 is more particularly intended to mechanically link, or even to interface, the resonator 2 and the frame 3 between them. The frame 3 is preferably fixed and non-deformable under mechanical constraints which it can undergo due to the vibratory deformations of the piezoelectric resonator 2 to which it is mechanically linked via the holding device 1.Thus, the holding device 1 and the frame 3 are intended to form together, for the resonator 2, a support that can be described as operational, in particular in relation to a targeted application of the resonator 2 and more particularly of its vibrations.

[0058] Preferably, the holding device 1 must be capable of holding at least one resonator 2, or even each resonator 2 among a plurality, at several connection (or contact) points 110. In this way, it is possible according to the present invention to isolate the piezoelectric resonator 2 from its working environment 3 while maintaining a relatively low loss rate due to the anchoring of the resonator 1. Consequently, it is possible according to the present invention to make the holding of the resonator 2 isostatic / hyperstatic relative to its support, which is not the case with the solutions of the prior art. Furthermore, the size of the support 2 should ideally be reduced to the strict minimum so that the total power density of the resonator 2 with its holding device 1 mounted on the frame 3 can be maximized, which is not the case of the solutions proposed by the patent document referenced CN 109546986 and by the article by BP Harrington et al...

[0059] By its nature, a piezoelectric resonator 2 generates, during operation, deformation waves which propagate to the frame 3 via the holding device 1. By correctly exploiting the waves produced, the deformation energy propagated to the frame 3 can be reduced and therefore the losses linked to the propagation of these waves reduced; this is what the holding device 1 achieves according to the first aspect of the present invention. In addition, by generating extended displacement nodes at the connection interfaces between the holding device 1 and the frame 3, mechanical isolation of the resonator from the frame is obtained. This makes it possible to avoid the resonance of elements of the frame which could cause an increase in the absorption of energy in the working frequency band.

[0060] As will become clear below, unlike the solutions of the prior art, the holding device 1 proposed here does not require an interface between the resonator 2 and the frame 3 on nodes with almost zero deformations. Consequently, the resonator 2 held by the holding device 1 according to the present invention can advantageously work on one of its primary vibration modes, where the exchangeable energy is maximum, for example the transverse mode, or more particularly the radial mode, of a resonator taking the form of a disc.

[0061] In addition, the holding device 1 according to the first aspect of the invention makes it possible to reduce the manufacturing costs of the assembly comprising the holding device 1 and the piezoelectric resonator 2.

[0062] Furthermore, it is of interest to employ simple resonator shapes 2, whether square, rectangular, circular, or disc-shaped or ring-shaped.

[0063] Also, potentially complex machining of the attachment 1 to minimize the energy transmitted by the resonator 2 to the frame 3 may be expensive to perform in the material from which the resonator 2 is made. Therefore, it is advantageous to be able to use a different material, less expensive and / or easier to machine, to manufacture the holding device 1. These materials may for example be brass, copper, plastic, ceramic, a glass fiber reinforced epoxy resin composite, such as FR-4 (for “Flame Retardant 4” in English), a crystal, etc.

[0064] Furthermore, the holding device 1 comprising at least two elementary cells 10a, 10b and 10c intended to be mechanically linked together and to be distributed over a periphery, internal or external, of the piezoelectric resonator 2, and at least one, preferably each, elementary cell 10a, 10b, 10c comprising four bars 11, 12, 13 and 14, the latter may be made of the same material or different materials and / or have varied sections (as well square as rectangular, circular, ...). Also, if the considerations below essentially relate to bars of rectangular section and made of the same material, the holding device 1 according to the first aspect of the invention is not limited to this example given for illustrative purposes.

[0065] An elementary cell 10a of the holding device 1 is shown diagrammatically in [Fig.l] which illustrates on the one hand the mechanical connection between the elementary cell 10a and the resonator 2, and on the other hand the mechanical connections between the elementary cell 10a and the frame 3. In [Fig.l], the piezoelectric resonator 2 to be held is only partially shown to have an enlarged view of the elementary cell 10a. Then, to generalize, we consider a perimeter of the resonator 2 developed, knowing that the shape of the resonator 2 can be round, square, rectangular, oval, that of a disc, that of a ring or any other. In [Fig.l], the elementary cell 10a is shown straight, but it can be curved, for example to follow a shape rounded edge of resonator 2.

[0066] Each elementary cell 10a, 10b, 10c, etc. of the attachment 1 can be seen as consisting of an assembly of three types of elementary vibrating bars, noted below Bu0Bul and Bu2, including a bar of a first type, called primary bar 11, two bars of the second type, called secondary bars 12 and 13, and a bar of a third type, called tertiary bar 14. The qualifiers “primary”, “secondary” and “tertiary” make it possible to discriminate between the types of bars, and not to establish levels of relative importance between types of bars.

[0067] At each connection point 110, noted below at, between an elementary cell 10a, 10b, 10c and the resonator 2, the elementary cell is mechanically connected to the resonator 2. In addition, each of the edges of the elementary cell 10a, i.e. each of the second ends 122 and 132 of the bars Bu], referenced 12 and 13 in [Fig.l], the elementary cell 10a is connected to the frame 3. These mechanical connections can be used to implement the resonator 2 and its attachment 1 in its working environment comprising the frame 3.

[0068] At least two elementary cells are distributed around the periphery of the resonator 2 to be held. In [Fig. 4], four holding devices 1 are shown which form, as we will see below, a structure closed on itself adapted to the circular periphery of a resonator 2 taking the form of a disc. It is nevertheless envisaged that such a closed structure can be made up of only two elementary cells. For example, starting from the example illustrated in [Fig. 4]. It is envisaged that a closed structure can be made up of two cells which, among the four shown in [Fig. 4], are opposite each other.

[0069] It is highly preferable that, at all the connection points 110 between the elementary cells 10a, 10b, 10c and 10d and the resonator 2, the resonator exerts substantially the same excitation when operating. To satisfy this preference, we will see below that, depending on the design (shape and dimensions) of the resonator 2 to be maintained and the vibration mode that one wishes to exploit, a minimum number of elementary cells to be distributed around the periphery of the resonator 2 may be highly desired, or even imposed. More particularly, the resonator 2 in operation exerts an excitation of substantially the same amplitude, for example to within 20%, preferably to within 10%, and / or substantially the same phase, to within 30° (or to within 0.52 radians), preferably to within 15°.For example, as developed below, for a resonator 2 taking the form of a disc on the circular periphery of which elementary cells 10a, 10b, 10c and 10d are to be distributed to form the holding device 1 according to the first aspect of the invention, it is preferable that the connection points 110 between the fixing 1 and the resonator 2 are substantially equally distributed, i.e. equidistant from the center of the resonator 2 and equidistant from their first neighbor(s). for example to within 20%, preferably to within 10%.

[0070] Preferably, with reference to figures 4 and 5, the holding device 1 comprises a plurality of elementary cells 10a, 10b, 10c and 10d, each comprising, or consisting of, an assembly of a primary bar 11, two secondary bars 12 and 13 and a tertiary bar 14, distributed around the periphery of the resonator 2 forming a structure closed on itself.

[0071] [Fig.2] represents two elementary cells 10a and 10b adjacent to each other (or consecutive), where appropriate in said structure closed on itself, which are mechanically connected to the resonator 2 on its periphery deforming along the y axis (Cf. [Fig.2]) when the resonator is in operation.

[0072] More particularly, the diagram of [Fig.2] illustrates so-called operating nodes, sometimes noted below nM and nu], including at least two nodes of a first type / Comprising for example the points referenced 1000 and 1100, and nodes of a second type nu0 comprising for example the points referenced 1200 and 1300. By primary bar 11, the two operating nodes 1000 and 1100 must preferably be respectively located in the oval zones in bold dashes which are illustrated in [Fig.3] at the ends 111 and 112 of each primary bar 11 and at the ends of each tertiary bar 14, and in particular between the primary bar 11 concerned and the tertiary bar 14 concerned. With reference to Figures 2 and 3, each operating node 1200 should preferably be located within a bold dashed oval area which is illustrated in [Fig.3] between the secondary bar 12 of a first of the two elementary cells illustrated and the secondary bar 13 of the adjacent elementary cell, and in particular to the right of a second end 122 of the first secondary bar 12 of the left elementary cell and to the right of the frame 3. Still with reference to Figures 2 and 3, each operating node 1300 must preferably be located in an oval zone in bold dashes which is illustrated in [Fig.3] between the secondary bar 13 of a first of the two elementary cells illustrated and the secondary bar 12 of the adjacent elementary cell, and in particular to the right of a second end 132 of the second secondary bar 13 of the cell 10a and to the right of the frame 3. The operating nodes 1200 and 1300 are preferably spaced apart from each other by less than 30%, advantageously less than 10%, of the excitation wavelength of the resonator 2 near ; they are preferably substantially confused with each other.This preference is encountered when the secondary bars have the same length, are linked two by two by one of their ends, and the secondary bars are mechanically linked to the frame 3 by the ends of the elementary cell to which they belong.

[0073] It is sought that these operating nodes 1000, 1100, 1200 and 1300 correspond to zones where the amplitude of deformation of the bars Bu0, Bui and Bu2 is almost zero for a determined excitation frequency of the resonator 2 taken in a determined frequency band, typically taken in its useful band, for example between its resonance frequency and its antiresonance frequency. For this, the primary 11 and secondary 12 and 13 bars of at least one elementary cell 10a, preferably of each elementary cell 10a, 10b, 10c, ..., can advantageously be dimensioned so that, for an excitation signal of the resonator 2 at the determined excitation frequency of the resonator 2, the operating nodes 1000, 1100, 1200 and 1300 are indeed found at the locations drawn in [Fig. 2] or more generally in a respective zone among the oval zones in bold dashes illustrated in [Fig. 3], to within 30%, advantageously 10%, of the excitation wavelength of the resonator 2.

[0074] Another way of expressing this desired technical effect consists of imposing, at these operating nodes 1000, 1100, 1200 and 1300, a movement of amplitude less than 10% of the maximum deformation amplitude generated in the secondary bars 12 and 13.

[0075] Once this first dimensioning has been carried out, or alternatively, the tertiary bar 14 of at least one elementary cell 10a, preferably the tertiary bar 14 of each elementary cell 10a, 10b, 10c, etc. is preferably dimensioned in order to promote the propagation of mechanical waves coming from the secondary bars 12 and 13 towards the tertiary bars 14 rather than towards the primary bars 11.

[0076] These desired technical effects, in order to minimize the mechanical energy transmitted by the resonator 2 to the frame 3 via the fixing 1, are achieved, thanks to the holding device 1 according to the first aspect of the invention, by exploiting three elementary principles presented briefly below, before being presented below in more detail.

[0077] With reference to Figure 3, the first principle to be exploited comes from the fact that the force Fa,^ transmitted by the vibrating resonator 2 to the primary bar(s) 11 is proportional to the mechanical impedance Z of the primary bar(s) 11 multiplied by the speed v of movement of the operating nodes 1000 and 1100 of the first type], this speed of movement being substantially equal to the speed of deformation of the excited piezoelectric resonator 2, due to the mechanical connections 110 between the fixing 1 and the resonator 2: F = Zy-

[0078] Since the aim is to limit as much as possible the energy transmitted by the resonator 2 to the frame 3 via the fixing 1, it is advantageous for the primary bars 11 to be dimensioned so that they are put into resonance with the vibrating resonator 2 to guarantee the existence of the nodes 1000 and 1100 of the first null type. To do this, the primary bars 11 should be dimensioned so that they have a quasi-zero mechanical impedance. The mechanical impedance Z can then be chosen such that that at the working frequency and for the maximum displacement generated at the periphery of the resonator, the power supplied by the resonator to the support is less than 30% of the power lost internally via its mechanical losses. The resonance of the elements 11 makes it possible to minimize the transmission of mechanical energy from these elements to the elements 12 and therefore ultimately the energy extracted from the resonator 2 by the holding device 1 in its working environment 3.

[0079] With reference to Figures 2 and 3, the second principle to be exploited consists of making the deformation waves induced at the levels of the consecutive mechanical connections, sometimes noted below as au and au+I, between the elementary cells 10a and 10b and the resonator 2 interfere with each other. This advantageously contributes to confining the deformation waves so that they remain essentially in the fixing 1 and do not propagate to the frame 3 via the nodes nu0 of the second type. This function is performed by the secondary bars 12 and 13, sometimes noted below as Bul. Indeed, by making two deformation waves induced at the levels of two consecutive mechanical connections au and au+J interfere, it is ensured that the operating nodes 1200 and 1300 are extended zero displacement nodes.To do this, each of the first and second secondary bars 12 and 13 of at least one elementary cell 10a, preferably of each elementary cell 10a, 10b, 10c, ..., can be dimensioned so as to have a length substantially equal to a multiple of half a wavelength of the frequency, possibly average, of excitation of the resonator 2 and / or so as to have a quadratic moment, with respect to their longitudinal axis, at least four times greater, preferably at least ten times greater, than a quadratic moment of the primary bar 11 with respect to its longitudinal axis.

[0080] The third principle exploits the fact that the propagation of a deformation wave from a primary bar Bu0 to a secondary bar Bul is not equivalent to that of a wave from a secondary bar Bul to a primary bar Bu0. The exploitation of this third principle aims here again in particular to minimize the interference of deformation waves which would lead to an increase in the transfer of energy from the resonator 2 to the frame 3 via the fixing 1. This objective is essentially achieved by dimensioning the tertiary bars Bu2. More particularly, to achieve the set objective, each tertiary bar 14 can: a. have a length substantially equal to the length of the primary bar 11, and / or b. have a thickness (or more generally a cross-sectional area) greater, preferably at least twice greater, than a thickness (or more generally a cross-sectional area) of the primary bar 11, and / or c. be matched in mechanical impedance with the first and second bars secondary 12 and 13.

[0081] We return below in more detail to each of the three principles introduced above.

[0082] Minimization of the energy transfer between the frame and the resonator by the primary bars B„n

[0083] At the contact points 110 between the holding device 1 and the resonator 2, these points being noted below as au and au+i for two adjacent elementary cells u and u + 1, transverse mechanical waves of amplitude AE0 are generated at the pulsation w in the material constituting the holding device 1 and therefore first in the bars and Here, the whole of the holding device 1 is intended to operate with a resonator 2 working on a well-defined frequency range, between its resonance frequency and its antiresonance frequency on a chosen mode; the interval including the deformation pulsation œ is therefore known.

[0084] Initially, we will only consider that the deformation wave induced at each of the connection points au, au+[, etc. is substantially identical. Indeed, we can consider that all of the points of application of the deformation, i.e. the connection points au, au+[, etc., behave rigorously in the same way by hypothesis of placement of said points relative to the resonator 2, and more particularly relative to its periphery. Thus, we can consider the resonator 2 as a displacement generator Ay of amplitude AE0 at au(+i), such that:

[0085] [Math.l] Avfa^yf) = , etc.

[0086] In order to generate a mainly transverse mechanical wave in the fixing 1, the primary bar 11, denoted Bu0, playing the role of a support rod, must be substantially in a tangential direction, to within 40°, preferably to within 20°, to the local periphery of the resonator 2, knowing that the primary bar 11 may itself have a curvature. This support rod Bu0 must have a main resonance mode close to the deformation pulsation 60 with respect to its excitation in au(+1), and in particular with regard to the direction of this excitation; typically, if the resonator 2 has a transverse movement, and for example radial, and the primary bar 11 is at least locally tangential to the periphery of the resonator 2, then the primary bar 11 operates essentially in bending mode, and it is then necessary to consider the mode main resonance in bending mode. Then, at the same resonant frequency, ty sting at the same parameter value where m is the equivalent mass reduced to end of beam of the primary bar 11 and where k is its stiffness, the more said mass is weak, the lower the stiffness, the lower the forces transmitted by this stiffness. Thus, among the possible geometric solutions for the primary bar 11, it is advantageous to take the smallest. This optimal choice with regard to the transmission of mechanical forces is however limited by: a. Manufacturing possibilities, for example regarding the minimum thickness that can be achieved according to the selected manufacturing process and the cost of the associated precision / fineness, b. Mechanical constraints in primary bar 1, and c. The robustness of the primary bar 11, and more generally of the fixing 1 (shock resistance for example).

[0087] To minimize the mechanical stresses in the material constituting the primary bar 11, it is advantageous for its displacement amplitude to be small compared to the thickness of the primary bar 11; typically, a thickness of primary bar 11 will be chosen which is at least 10 times greater than the deformation amplitude, for example average, of the piezoelectric resonator in its excitation frequency band.

[0088] Considering each primary bar 11 as a beam excited in a bending mode, the energy transmitted to the holding device 1 over an operating period T at the level of the primary bar 11 depends both on the speed of the movement of the primary bar, which is imposed by the resonator 2, and on the force that the primary bar 11 will generate in opposition to its movement:

[0089] [Math.2] Transmitted ( + 0) 1) ) + ( ^«(+1)

[0090] It is then understood that minimizing the opposing force of each primary bar 11 at its point of displacement makes it possible to reduce the total energy supplied to the rest of the holding device 1 by the resonator 2.

[0091] This is the first principle brought into play in the context of the dimensioning of the binding 1 according to the first aspect of the invention, and which aims to minimize the energy supplied to the rest of the binding 1 by its first primary bars 11. The stiffness opposed by the primary bars 11 on the resonator 2 must therefore be low. In the case of the use of primary bars 11 used in bending mode, reducing their quadratic moment 1 makes it possible to reduce the opposing force and thus minimize the energy transmitted to the binding 1 by the resonator 2. Also, making the primary bars 11 enter into resonance at the excitation frequency of the resonator 2 makes it possible to reduce the equivalent stiffness of these bars 11 and therefore the energy transmitted to the rest of the binding 1. It is therefore interesting to develop primary bars 11 such that they resonate at the operating frequency of the resonator 2 and accompany its movement.

[0092] The sizing of the primary bars 11 is therefore carried out so that they enter into resonance for a frequency located in the working frequency band of the resonator 2. We will also seek to make each primary bar 11 resonate on a first mode. In this way, we try to limit as much as possible the presence of other resonance modes which could come to oppose the movement of the primary bars 11 in the working range between the resonance frequency and the antiresonance frequency of the resonator 2.

[0093] Subsequently, an attempt is made to minimize the energy transmitted from the primary bars 11 to the secondary bars 12. Knowing that the primary bars 11 are in resonance or close to resonance (to within 20%, advantageously to within 10%) at the working frequency of the resonator 2, quasi-nodes, i.e. points (or zones) where the displacement of the developed transverse wave is very low, are generated at the level of the two operating nodes 1000 and 1100 linked to each primary bar 11. In fact, at these locations, the stresses generated by the mechanical deformation waves are maximum for each primary bar 11.However, if the secondary bars 12 and 13 mechanically linked to each primary bar 11 have a greater quadratic moment, for example due to a thickness greater than that of the primary bar 11, the displacement of the secondary bars 12 and 13 produced by the displacement of the primary bar 11 of each elementary cell is lower at iso-stress. Thus, due to a break in linear stiffness between the primary bar 11 and the secondary bars 12 and 13 of each elementary cell, most of the energy supplied by the resonator 2 remains confined at the level of the primary bar 11 and propagates little to the rest of the attachment. It is moreover by reflecting the transverse deformation wave at the level of the two operating nodes 1000 and 1100 that the primary bar 11 of each elementary cell enters into resonance.

[0094] Interference of deformation waves for their confinement by the secondary bars B^

[0095] Due to the distribution, preferably substantially symmetrical, or even periodic, of the elementary cells 10a, 10b, 10c, etc. of the holding device 1, or even by the periodic structure that it forms, relative to the periphery of the resonator 2, the holding device 1 induces interference within it between the deformation waves produced at two consecutive connection points 110 au and a(u+1) with the resonator 2. Indeed, the waves which enter at these consecutive connection points 110 au and a(u+i) propagate on the primary bars 11, Bu0 and B(u+ij0, of two consecutive elementary cells, over a distance equivalent, in the propagation medium, to a quarter of the excitation wavelength of the resonator 2, forming quasi-nodes at the operating nodes 1000 and 1100 of the first null type. Then the waves propagate on the secondary bars 12 and 13 to finally meet at the operating nodes 1200 and 1300 of the second type nu0 which are substantially merged with each other and located between two consecutive elementary cells 10a and 10b.

[0096] By choosing secondary bars 12 and 13 having a length substantially equal to a multiple of half a wavelength, then the meeting of these waves at the operating nodes 1200 and 1300 of the second type nu0 is carried out by interference of a destructive nature between the waves (see equations below). Finally, the induced phase shift creates a zero displacement node extended to the levels of the operating nodes 1200 and 1300 of the second type nu0.

[0097] An extended zero displacement node is defined here as an enlarged zone (represented for the example, in [Fig. 3], by each of the oval zones in bold dashes) in which the displacement is substantially zero, typically, over a distance of X / 10, where X is the possibly average wavelength of deformation. The displacement at an extended zero displacement node is preferably at least 10 times less than the maximum displacement at the point of maximum displacement of the fixing 1. This makes it possible to be tolerant on the effective anchoring point to the frame 3, as well as on the working frequency induced by the vibration of the resonator 2. This is particularly necessary in the case of the use of a strongly coupled piezoelectric resonator 2 which can be made to operate over a wide frequency range (typically 20% frequency variation).The extended zero displacement nodes are obtained at the interconnection points 1200 and 1300 of the second type nu0, limiting the transmission of waves towards the frame 3 at these nodes 1200 and 1300. Due to the repetitive, even periodic, structure of the attachment 1, the effect produced at the operating nodes 1200 and 1300 which are located between the two consecutive elementary cells 10a and 10b partially illustrated in [Fig.2], is also obtained on the operating nodes 1200 and 1300 which are located between two other consecutive elementary cells in the structure formed by the attachment 1. These operating nodes 1200 and 1300 of the second type nM can be noted below: n(u.])0, n(u+])0, etc. .

[0098] Following the same reflection conducted on the interference of the waves generated at the contact points 110 between the holding device 1 and the resonator 2, it can be said that, by construction, each secondary bar 12 and 13 of each elementary cell 10a, 10b, 10c, etc. obtains a stiffer relative stiffness on the working frequency (where the nature of the interference is of the destructive type, that is to say that, for a certain internal constraint, the relative displacement will be lower than for the case of the propagation of a single wave in particular on its periphery). Thus, the confinement of the wave during its transmission between the primary bar 11 and the secondary bars 12 and 13 of each elementary cell is increased.

[0099] Finally, by taking up the general equation of the deflection in a beam in bending developed in the theory of Euler-Bernoulli beams, it is shown that the structure of the fixing 1 makes it possible to increase the relative stiffness of the secondary bars and produces nodes with zero displacement extended at the levels of the connections between the fixing 1 and the frame 3.

[0100] More particularly, the general equation for the transverse displacement of an excited beam at pulsation w can be written:

[0101] [Math.3] y (x, t) = ( Asin(Px) + Beos(Px) + Csinh(Px) + Dcosh(Px) ) y(x) = (Asin(Px) + Bcos(Px) + Csinh(Px) + Dcosh(Px) )

[0102] noting fi the wave number, 9? the phase shift, and A, B, C and D parameters depending on the boundary conditions imposed on the beam.

[0103] It is assumed that, by construction, the deformation waves emitted at the contact points 110 between the holding device 1 and the resonator 2 are substantially the same. Thus, at the operating nodes 1200 and 1300 of the second type n uo which are located between two consecutive elementary cells, the two waves will have traveled the same path, but in two opposite directions (x increasing or x decreasing in [Fig.2]). Assuming that the materials chosen for the secondary bars are substantially isotropic and that these bars are substantially of the same shape and dimensions, possibly with a symmetry of axis or plane, the deformations produced by these two waves are then substantially equivalent in amplitude.

[0104] Assuming that at the operating nodes 1000 and 1100 of the first type [nu], a node is indeed generated by the incident wave from the connection point 110 concerned and that the energy transmitted to the secondary bars 12 and 13 is low. On the one hand, we find embedding conditions at the level of the nodes [nu] and on the other hand, a point connection condition at the level of the nodes [nu0], because the holding device 1 is connected to the frame on its periphery at [nu0]. This gives us the following boundary conditions for calculating the deformation of the bars 12 and 13:

[0105] [Math.4] r«.(n„i) -0 3a "0

[0106] By placing oneself in a reference frame such as node 1100 of the elementary cell concerned is located at x = 0, and according to the assumptions of embedding at the level of node IlOO and of point connections at the level of nodes 1200 and 1300, the solution of the deformation of the secondary bars 12 and 13 is as follows:

[0107] [Math.5] Yau (x) = Ko ((cos (^x) - cosh (Px)) - 0.9825 (sinh (px) - sin (Px))) ^=3.927

[0108] Around the mechanical connection between the fixing 1 and the frame 3, therefore for x = l± + € with e small (Cf. figure 2), and more particularly for e less than 5% of we can write the deformation due to the deformation wave produced at the level of this connection in the following way:

[0109] Y^l^ e) = Y^icos^d^ e) ) -cosh(0(l1+ e) ) -0.9825(sinh(0(^ + e) ​​) - sin(0(^+ e) ) )) -O.9825(sinh(011)cosh(7j6) + cosh(^ / 1)sinh( / îe) -sin^ljcos^e) -cos(^i)sin(^e))) Ej / j+e) = y0((cos(^ / i) -^esin^) -coshC^J +^^(^)) -O.9825(sinh(j0Z1) +^ecosh(01]) -sin^Zj - (jecos( / ^l})J)+ O(e) y„a(7, + e) ​​~ y0( - / tesinlW ) -0.9825( / Jecosh( 01j - / 16008(^) ) )

[0110] For the wave propagating in the opposite direction, i.e. from the connection point au+] of the adjacent elementary cell to the operating nodes 1200 and 1300 of the second type nu0, we find [Math.6] x — 1^- e around the mechanical connection with the frame 3. It is then possible to write the corresponding formula and calculate the superposition of the two deformation waves coming from the connection points au and au+1 of the two elementary cells concerned around their meeting point [Math.6] [YES] [Math.7] Ylot{nuG) = YaÀA + e) ​​+ Yau{lr e) Ym-^ + 0( 6)

[0112] It can therefore be said that, around each of the operating nodes 1200 and 1300 of the second type nu0, extended nuis displacement nodes are induced due to the repetition, possibly periodic, of the elementary cells 10a, 10b, 10c, etc. As the vibration around the operating nodes 1200 and 1300 is therefore very weak, it hardly propagates to the rest of the frame 3 and remains confined in the fixing 1.

[0113] Then, with reference to [Fig.2], we can consider that the wave emitted at the point of connection 110, (noted au+]), following a first connection point 110, noted au, will continue to interfere with the wave emitted at the first connection point 110 (noted in the secondary bar 13 of the elementary cell 10a and, conversely, the wave emitted at the first connection point 110, noted au, will interfere with the wave emitted from the second connection point a„+i in the secondary bar 12 of the second elementary cell 10b.

[0114] As previously, the interference is of a destructive nature which tends to limit the amplitude of displacement of the secondary bars 12 and 13 and therefore contributes to minimizing losses which are functions of the quantity of material displaced.

[0115] This phenomenon is illustrated in [Fig.3]. We can observe: a. in long-short dashes, a first deformation wave generated by the fixation point at, and b. dotted, a second deformation wave generated by the fixation point at +j.

[0116] The superposition of the two waves, in the simplified case of a medium without dissipation with bars sized in the manner explained previously, is represented by dashes. It is then noted that, in the set of secondary bars 12 and 13, the deformation waves interfere and cancel each other out. However, the stress within them, in particular on their ends, remains significant. It can therefore be said that the relative stiffness of the secondary bars 12 and 13 is increased, which limits the propagation of the deformation waves generated at the fixing points at and at +1 towards the secondary bars 12 and 13 located between the fixing points at and at +1.

[0117] Anisotropic propagation medium for transverse waves between the primary bars / Ç, and secondary B^ by the tertiary bars

[0118] Through the diagram of [Fig.3], we understand the interest of the tertiary bars 14 which create favorable propagation paths for the deformation waves coming from the mechanical connections of the attachment 1 to the frame 3 towards the operating nodes 1000 and 1100 of the first null type (Cf. the waves represented in the bars 14 illustrated in [Fig.3]). The presence of such paths is highly preferable because, in view of the phase shifts imposed by the proposed attachment 1, the deformation waves at the connection points au and au+1 would find themselves in destructive interference with the waves arriving / re coming from the primary bars 11, this having the consequence of increasing the relative stiffness of the primary bars 11 and therefore increasing the energy transfer between the attachment 1 and the piezoelectric resonator 2.For this reason, it is proposed to create a more favorable propagation path (i.e. having an equivalent linear stiffness), such that the deformation base propagates mainly in this path. To maximize the transfer of deformation base between the secondary bars 12 and 13 and the tertiary 14, it is therefore . preferable that these are matched in impedance. However, as by destructive interference the secondary bars 12 and 13 are made very stiff at the working frequency (see above), we will seek to produce tertiary bars 14 such that their quadratic moment relative to the working axis is much greater than in the primary bars 11.

[0119] By doing so, the waves generated by the fixing points au and au+i considered will not modify the equivalent stiffness of the primary bars 11, which will therefore not cause any modification to the power transfer from the resonator 2 to the frame 3 (transfer which must remain minimal).

[0120] Dimensioning update

[0121] It is preferable that attention be paid to the distance between the connection points au and au+i between the attachment 1 and the resonator 2. Indeed, if the connection points au and au+i are located at distances such that the total distance Ltot between two connection points is equal to or a multiple of half a wavelength that can be generated on the periphery of the resonator 2 in the working frequency band, a favored resonance can appear on the contours thereof. For example, in the case of disk-type resonators, if three contact points are used while the latter operates in a radial mode, then the distance of the points two by two is = 221^ with R the radius of the resonator 2. Now 2R corresponds to the main working characteristic length. As L[ot is close to this length, it can be assumed that a favorable contour mode can be excited, which is not desired.We will therefore prefer to work with four elementary cells and therefore four fixing points of resonator 2 on fixing 1.

[0122] The proposed invention is therefore based on three distinct principles which are: a. minimize the energy transmitted to the attachment 1 by the resonator 2 by using a primary bar that is not very stiff at the working frequency, b. developing substantially zero displacement connection nodes extended at the mechanical junctions between consecutive cells which make it possible to interface the attachment 1 with the frame 3 and thus to isolate the resonator 2 from its working environment 3, and c. create favorable propagation paths via the tertiary bar 14 such that the mechanical basis of deformation generated by a neighboring anchor cannot interfere with the primary bar 11.

[0123] As seen above, to minimize the energy transmitted from the resonator 2 to the attachment 1, the primary bars 11 are sized to resonate at a frequency in the working frequency range of the resonator. The primary bars 11 are as if embedded-embedded substantially at the level of the function nodes operation 1000 and 1100 of the first bare type], and each attachment point of the resonator 2 to the attachment 1 is substantially located in the middle of the primary bar 11 which carries it. The resonance frequency of these primary bars 11 is chosen so that it corresponds to their main mode of resonance by considering each primary bar 11 in itself, i.e. not mechanically linked to the resonator 2. For more precision in the dimensioning of the primary bars 11, the possible connection pad or lug 110 can be included, at least the mass of this pad, so that the “primary bar 11 + connection pad” assembly resonates well at the desired frequency. Furthermore, in addition to respecting the resonance frequency, each primary bar 11 is chosen to be as flexible as possible within the limits of technical and economic possibilities, in order to further limit the energy transmitted to the attachment 1.

[0124] Furthermore, by creating a break in the mechanical transmission impedance at the operating nodes 1000 and 1100 of the first zero type, little energy is transmitted to the rest of the fixing 1, i.e. to the assembly formed by the primary 11 and tertiary 14 bars.

[0125] Then, by producing the holding device 1 in a symmetrical, or even periodic, manner around the resonator 2, the deformation waves produced in the fixing 1 are put into destructive interference which makes it possible both to increase the equivalent stiffness of the secondary bars 12 and 13, but also to create connection nodes with extended nuisance displacements at the levels of the mechanical connections between consecutive elementary cells. It is these operating nodes 1200 and 1300 of the second type nM which are advantageously used to mechanically interface the fixing 1 with the frame 3.

[0126] Finally, so that the deformation waves circulating in the secondary bars 12 and 13 do not disturb and increase the equivalent stiffness of the primary bars 11, which would increase the energy supplied to the fixing 1 by the resonator 2, the propagation of the deformation waves between the primary bars 11 and the secondary bars 12 and 13 is minimized via the use of the tertiary bars 14 as waveguides which represent more favorable energy transfer paths. Indeed, the thickness of the tertiary bars 14 can be chosen to be large compared to the thickness of the primary bars 11. Ideally, each tertiary bar 14 is matched in mechanical impedance with the secondary bars 12 and 13 so that most of the energy coming from the secondary bars is absorbed by the tertiary bars 14 and not by the primary bars 11.In fact, as the stiffness of the secondary bars 12 and 13 is increased at the operating frequency by destructive interference, we will seek to make the tertiary bars 14 stiffer than the primary bars 11. As for the primary bars 11, to minimize . their stiffness, they are preferably chosen to be thin compared to the thickness of the secondary bars 12 and 13, which accentuates the break in mechanical impedance and limits the energy exchanges between primary bars 11 and secondary bars 12 and 13, which is also advantageous.

[0127] The proposed invention addresses the main problem of mechanically holding / maintaining a piezoelectric resonator 2 while limiting the impact of its holding device 1 for working modes of the longitudinal and / or transverse resonance type. Unlike the solutions mentioned in the introduction, the holding device 1 according to the first aspect of the invention uses the interference of the waves propagating within it to minimize the energy transferred from the resonator to the frame 3 and to create extended nodes facilitating the connection of the holding device 1 to the frame 3, while limiting the transfer of energy to the frame 3. In doing so, the dimensions of the holding device 1 can be considerably reduced. The very principle of the holding device 1 described above can be adapted to several geometries (dimensions and shape) of resonators 2 and can be made of several different materials.

[0128] The following part presents, by way of example, calculation rules for the dimensioning of a holding device 1 adapted to a resonator 2 taking the form of a disc.

[0129] Case of a disk-type resonator operating on a main radial-type mode

[0130] A fixing device 1 according to the first aspect of the invention is given below. below, for the example, which allows to maintain a piezoelectric resonator 2 of circular shape operating on a radial type vibration mode. In order to maintain the resonator 2 in a minimally isostatic manner, a minimum of three attachment points 110 are necessary. However, as seen previously, the distance between the attachment points 110 on the periphery of the resonator 2 is then ^2R, and, as is close to 1, we can easily assume that a diametrical mode will interfere in our operating band between the resonance frequency and the antiresonance frequency of the resonator 2. A solution consists of the addition of a fourth attachment point 110 which reduces the distance between the attachment points and allows to isolate the diametrical resonance mode at a higher frequency far from the operating band. With four attachment points, the holding device 1 can be as illustrated in [Fig.4]

[0131] The first important parameters to consider are the working frequency band of the developed attachment 1 and also the dimension Ltot available for the production of an elementary cell (or pattern) of the holding device 1. These two parameters are directly linked to the choice of the resonant piezoelectric material and to its dimensions.

[0132] In the present example, we dimension below the holding device 1 for a circular resonator of 25mm diameter made of a piezoelectric material based on PZT (for lead zirconate titanoates) known under the commercial name C213 from Fujiceramic®. This resonator then has a resonance frequency of 89kHz and an antiresonance frequency of 103kHz. It is therefore to this frequency range that the bars 11, 12, 13 and 14 of each elementary cell 10a, 10b, 10c and 10d of the holding device 1 will have to be adapted. In addition, as we have opted for four holding points, we know that for a holding device 1 located at an average distance of 1.5 mm from the circular outer periphery of the resonator, we have Ltot = 22mm.

[0133] The choice of the material constituting the holding device 1 can then come. A material commonly used in electronics is FR-4 TGI50. Its advantage is that it has good dielectric properties and can be purchased in copper-coated plates. This makes it possible to obtain two parallel conductive planes electrically insulated from each other which are useful for resuming electrical contacts between the piezoelectric resonator 2 and the frame 3 through the fixing 1.

[0134] FR-4 TG150 has a Young's modulus E of 22GPa and a density g of 1900kg / m3. In an effort to simplify the process, it was chosen to use standard FR-4 plates which have a height of 1.55mm and which are covered with a 70pm thick layer of copper. As the thickness of the copper is small compared to the height of the FR-4, only FR-4 will be considered for mechanical dimensioning. In addition, although it is a composite material, it will be considered as isotropic for the dimensioning of the Bu0, Bu] and Bu2 bars. In addition, for the example, only rectangular section bars will be considered, which are simpler to produce when machining an FR-4 plate with a milling cutter or a laser.

[0135] Sizing of primary bars Bhq

[0136] The first set of bars to be dimensioned corresponds to the set of primary bars, referenced 11 and noted Bu0. Indeed, their length and their thickness will dimension the whole of the rest of the holding device 1. Thus, let us suppose that, for manufacturing reasons, the thickness (along y in the diagram of figure 1) of the primary bars B„o is e0 = 0.5 mm. It is then necessary to calculate their length so that they can enter into resonance at a frequency included in the chosen operating / working band of the resonator 2. The methods for determining the deformation of beams in dynamics are formulated through the theory of Euler-Bernoulli beams, the fundamental equation of a beam in bending along the y axis is then the following:

[0137] [Math. 8] PS àv» + -f(X^)

[0138] With A the associated quadratic bending moment, S the section of the beam, 7 the displacement and f the external force density. In our case, as we apply a force punctually, we will consider the external force density zero. In addition, we know in advance that we will seek to make our beam, and more particularly our primary bar 11, resonate in its first mode and knowing that it will be linked at its center to the resonator 2. As each elementary cell 10a, 10b, 10c and 10d is perfectly symmetrical, the boundary conditions are the same. The solutions to the above equation are then of the form:

[0139] [Math.9] t) = (Asm(flx) +Bcos(0x) + Csinh(0x) + Dcosh(fix)

[0140] [Math. 10]

[0141] By construction hypothesis, the primary bar, referenced 11 noted Bu0, is considered to be embedded on its two ends. Thus, at the limits of the primary bar 11, we can consider almost zero transverse and angular displacements. We therefore have:

[0142] [Math. 11] XxwJ' 0 -0

[0143] Knowing the boundary conditions, and the form of the solution previously introduced, we find that the natural pulsations of each primary bar 11 are the solutions of the equation:

[0144] [Math. 12] tan^ / 0 + tanh / î / 0 = 0

[0145] The solution of the first vibration mode which corresponds to the mode that we seek to implement is then given by the following equations:

[0146] [Math. 13] = 4.73 I _ 4.73 4 9 t

[0147] Knowing the thickness (0.5mm) and the height of the bars (1.55mm), their flexural modulus and their section can be calculated as:

[0148] [Math. 14] So - he^

[0149] Using the formula described above and considering a resonance frequency of the bar of 95kHz (i.e. a pulsation included in the working frequency band). We find a length l0 of the primary bars Bll0 equal to 4.3mm.

[0150] Sizing of secondary bars B^

[0151] Since the architecture of the holding device is periodic, we seek to loop the elementary cell. Thus, in the case where we consider that the holding device 1 is located at a distance of approximately 1.5 mm from the radius of the resonator 2 and that this is repeated 4 times, we then find that the average available length is given by:

[0152] [Math. 15] Ltof=(7^+1.5e-3)*2*^ , where Rpr is the radius of resonator 2.

[0153] In our example, we find here Ltot which is equal to 22mm. Considering that a portion of 4.3mm is already used by the primary bar of each elementary cell, we know that the two secondary bars 12 and 13 of each elementary cell total a length of 17.7mm. Thus, the length l, of a single secondary bar Bul is 8.85mm. In this way, the holding device 1 loops back on itself around the resonator 2.

[0154] The secondary bars 12 and 13 are connected on their periphery to the frame 3 at the operating nodes 1200 and 1300. The connection between the secondary bars 12 and 13 and the frame 3 is considered to be punctual. In addition, the bars are held on their second side via a bar considered to be very rigid substantially at a zero displacement node 1000 or 1100. Thus the bars B „7 are considered to be embedded on the one hand and connected punctually on the other hand. By reusing the equations developed above and the equation for the bending modulus, the thickness of the bars Buj can be calculated such that it corresponds to a half-wavelength at a frequency taken in the operating band of the resonator 2, and preferably taken substantially at its center or its geometric center:

[0155] [Math. 16]

[0156] Thus in our example case, we find that the secondary bars Bu] have a thickness of 3.4 mm for an average radius of curvature of 14.5 mm relative to the center of resonator 2. With these dimensions, extended zero displacement nodes are created at the points nu0 of attachment of the holding device 1 to the frame 3.

[0157] Sizing of tertiary bars B^,

[0158] As for the last type of bars of the elementary cells of the holding device 1, i.e. the tertiary bars 14, denoted Bu2, it is sought to make it impedance-matched with respect to the secondary bars Bu], so that the deformation waves propagating from the secondary bars Bu] towards the tertiary bars Bu2 and primary bars Bu0 propagate mainly in the tertiary bars Bu2 and little in the primary bars Bu0. However, in the secondary bars Bu1, the deformation waves are put into destructive interference which makes these bars very rigid at the frequency of study. Finally, in order to be impedance-matched, the tertiary bars Bu2 would also have to be rigid which would result in very thick bars. We will therefore just seek to find a thickness of these tertiary bars Bu2 such that their quadratic moment is much greater than the quadratic moment of the primary bars Bu0.For example, we can consider a factor of 10 (at least 4 and advantageously more than 10). We are therefore looking for: .

[0159] [Math. 17] Zz(B„2) = 10 / ,(¾) ^2 = ^0

[0160] We then find that all of the tertiary bars Bu2 will have a thickness of 1.07 mm according to this criterion. Of course, the ratio 10 is not fixed and other factors can be used, in particular if we seek to reduce the surface area used by the holding device 1 or to make the holding device 1 even more efficient by making the tertiary bars Bu2 even more rigid.

[0161] [Fig.4] represents the support dimensioned using the above criteria. By using the copper layers present on the FR-4, electrical connection tracks connecting the upper electrode of the resonator with the frame can be made in a simple manner using conventional methods for manufacturing printed circuit boards often called PCBs (for Printed Circuit Boards in English). In the same way, tracks connecting the lower electrode of the resonator with the frame can also be manufactured.

[0162] The frame may be a continuation of the material used for the attachment, for example, in the case of using a PCB as described in this example, the PCB may continue to accommodate the resonator drive electronics and other electronic functions.

[0163] Through the example given above, we have given the dimensioning of a holding device 1 for a circular type resonator 2. The approach is applicable for other forms of resonators 2, but also with other forms of bars 11, 12, 13 and 14, we can consider bars of circular section, of IPN type or made of different materials.

[0164] An alternative to the example given above consists of not working with a circular resonator 2 but with a resonator having any shape. By correctly using the approach presented above, it is then possible, for a person skilled in the art, to correctly size the three types of elementary bars constituting the holding device 1 according to the first aspect of the invention, so that the latter holds the resonator 2 while producing few losses and transmitting little energy to the frame 3. These three types of elementary bars are not necessarily of square sections, but can have other shapes of sections: IPN, round, trapezoidal, etc. In addition, the three types of bars Bu0, Bu] and Bu2 can be manufactured from different materials.

[0165] Another alternative consists of not placing the holding device 1 on the outer edge of the resonator 2, but on either side of it, on these flat faces. In doing so, it is possible to use materials which are directly electrical conductors (for example brass) and which have better mechanical properties. The only constraint for the placement of the connection points between the holding device 1 and the resonator 2 is that, at these points, the holding device 1 undergoes transverse deformations substantially in phase (within 30°) and substantially of the same amplitude (within 20%).

[0166] It is also possible to place the fixing device 1 on the internal part of a resonator 2 taking the form of a hollow disc or ring, and not necessarily along the external perimeter thereof, as is the case in the example given above. Similarly, the resonator 2 may have the form of a washer / tube and this washer / tube may be mechanically held by a holding device 1 according to the first aspect of the invention by its internal perimeter.

[0167] Furthermore, in the case of the use of a piezoelectric resonator 2 for energy conversion, it is possible to produce the fixing device 1 directly in the material serving as support for the electronic circuit (ceramic, PCB).

[0168] It is also possible to make the fixing 1 in the same material as the resonator 2, and in particular in continuity with it.

[0169] Another alternative consists of using the holding device 1 in matrix form for a multitude of resonators 2. Thus, the interference of the acoustic waves is no longer necessarily produced only by the mechanical connection points of a single resonator, but also by the mechanical connection points of other resonators 2, having for example substantially the same characteristics. The advantage of working in matrix format is to be able to work at high frequency, this being defined by the dimension of the resonator 25 while using a large surface area of ​​resonators 2, which makes it possible to increase the power of a converter comprising the holding device 1 in matrix form. [Fig.5] shows a diagram of the implementation of such a matrix structure.

[0170] The holding device 1 was first designed for power electronics and the use of massive piezoelectric resonators 2. It forms an interesting assembly with the piezoelectric resonator component 2 and allows its use to be made more massive. As stated in the introduction, power converters are omnipresent and their frequency increase poses problems. If the solution of using piezoelectric resonators 2 proves to be truly relevant, the holding device according to the first aspect of the invention removes the obstacle of “how to implement these vibrating components” without disturbing their vibration and without transmitting vibrations to the frame 3.

[0171] It should also be noted that it is entirely possible to use the holding device 1 according to the first aspect of the invention on radiofrequency systems, rather than on power converters. This would also make it possible to reduce their surface footprint.

[0172] The invention is not limited to the embodiments previously described and extends to all embodiments covered by the invention.

Claims

Claims

1. Holding device (1) for piezoelectric resonator (2), the holding device (1) comprising at least two elementary cells (10a, 10b and 10c) intended to be mechanically linked together and to be distributed around a periphery of the piezoelectric resonator (2), at least one, preferably each, elementary cell (10a, 10b, 10c) comprising four bars (11, 12, 13 and 14) including: • a so-called primary bar (11) by which the holding device (1) is intended to be mechanically linked to the piezoelectric resonator (2), • two so-called secondary bars (12 and 13), including: i. a first secondary bar (12):

1. mechanically linked to the primary bar (11) of the elementary cell (10a) considered, 2. mechanically linked to an elementary cell (10b or 10c) adjacent to the elementary cell (10a) considered, and 3. intended to be mechanically linked to an external frame (3), and ii. a second secondary bar (13):

1. mechanically linked to the primary bar (11) of the elementary cell (10a) considered, 2. mechanically linked to an elementary cell (10b or 10c) adjacent to the elementary cell (10a) considered, and 3. intended to be mechanically linked to the external frame (3), and • a so-called tertiary bar (14) mechanically linking together the first secondary bar (12) and the second secondary bar (13) of the elementary cell (10a) considered.

2. Holding device according to the preceding claim, in which at least one, preferably each, primary bar (11) of at least one, preferably each, elementary cell (10a, 10b, 10c) is of dimensions such that, with a piezoelectric resonator (2) configured to vibrate in a determined frequency band, the primary bar (11) is in resonance, to within 20%, advantageously to within 10%, with the vibrations of the piezoelectric resonator (2) for any excitation frequency located in said determined frequency band.

3. Holding device according to any one of the preceding claims, in which at least one, preferably each, of the first and second secondary bars (12 and 13) of at least one, preferably each, elementary cell (10a, 10b, 10c) is of dimensions such that it has a length substantially equal to a multiple of half a wavelength for a chosen excitation frequency located in the determined frequency band, and preferably at its center or at its geometric center, and have, with respect to their longitudinal axis, a quadratic moment at least four times greater, preferably at least ten times greater, than a quadratic moment of the primary bar (11) with respect to its longitudinal axis.

4. Holding device according to any one of the preceding claims, in which the tertiary bar (14) of at least one, preferably each, elementary cell (10a, 10b, 10c), is of dimensions such that it has a length substantially equal to the length of the primary bar (11) of the elementary cell considered, a thickness greater, preferably at least twice greater, than a thickness of the primary bar (11) of the elementary cell considered, and is matched in mechanical impedance with the first and second secondary bars (12 and 13) of the elementary cell considered.

5. Holding device according to any one of the preceding claims, wherein said at least two elementary cells (10a, 10b and 10c) are intended to be distributed around the periphery of the piezoelectric resonator (2) forming a structure closed on itself, the elementary cell (10b or 10c) which is mechanically linked to the first secondary bar (12) of the elementary cell (10a) considered, is adjacent, in said closed structure, to the elementary cell (10a) considered, and the elementary cell (10b or 10c) which is mechanically linked to the second secondary bar (13) of the elementary cell (10a) considered, is adjacent, in said closed structure, to the elementary cell (10a) considered, the elementary cells mechanically linked to the elementary cell (10a) considered being able to be different from each other.

6. Holding device according to any one of claims 2 to 5, in which the primary bar (11) is sized so as to resonate in a first mode, to within 20%, advantageously to within 10%, for said frequency located in the determined frequency band.

7. A holding device according to any one of claims 1 to 6, wherein at least one bar, preferably each bar, among the four bars (11, 12, 13 and 14) is made from at least one material, preferably isotropic, chosen from: • a metal, such as brass or copper, • plastic, • a ceramic, • a crystal and • a glass fiber reinforced epoxy resin composite, such as FR-4.

8. A holding device according to claims 1 to 6, wherein at least one bar, preferably each bar, of the four bars (11, 12, 13 and 14) comprises an insulating material and one or more thin metal layers separated by the insulating material, for example a printed circuit board.

9. Holding device according to claims 1 to 6, in which at least one bar, preferably each bar, is made from the same piezoelectric material, preferably transverse isotropic, as that from which the piezoelectric resonator (2) is intended to be made.

10. Holding device according to any one of the preceding claims, in which the primary bar (11) is intended to be mechanically linked to the piezoelectric resonator (2) at a first linking point (110) located substantially between a first end (111) and a second end (112) of the primary bar (112).

11. Holding device according to any one of the preceding claims, in which the primary bar (11) is intended to be mechanically linked to the piezoelectric resonator (2) by means of a lug (110), the mass of the lug (110) being taken into account where appropriate for the dimensioning of the primary bar (11).

12. A holding device according to any one of the preceding claims- preceding, in which: • the first secondary bar (12) of the elementary cell (10a) considered is mechanically linked by a first (121) of its two ends (121 and 122) to the first end (111) of the primary bar (11) of the elementary cell (10a) considered, is mechanically linked by a second (122) of its two ends (121 and 122) at the same time to a second end (132) of the secondary bar (13) of an elementary cell (10b or 10c) which, among said at least two elementary cells (10a, 10b and 10c), is adjacent to the elementary cell (10a) considered, and is intended to be mechanically linked to the external frame (3), and • the second secondary bar (13) of the elementary cell (10a) considered is mechanically linked by a first (131) of its two ends (131 and 132) at the second end (112) of the primary bar (11) of the elementary cell (10a) considered,is mechanically linked by a second (132) of its two ends (131 and 132) to both a second end (122) of the first secondary bar (12) of an elementary cell (10b or 10c) which, among said at least two elementary cells (10a, 10b and 10c), is adjacent to the elementary cell (10a) considered, and intended to be mechanically linked to the external frame (3).,

13. Holding device according to the preceding claim, in which the tertiary bar (14) of the elementary cell (10a) considered mechanically connects together the first end (121) of the first secondary bar (12) of the elementary cell (10a) considered and the first end (131) of the second secondary bar (13) of the elementary cell (10a) considered.

14. Holding device according to any one of the preceding claims, in which the tertiary bar (14) of each elementary cell (10a, 10b, 10c) is located in line with and at a distance from the primary bar (11) of the elementary cell (10a) in question, and is intended to be located, relative to the outer or inner periphery of the piezoelectric resonator (2) which it contributes to holding, at a greater distance than the primary bar (11) of the elementary cell (10a). considered.

15. Holding device according to any one of the preceding claims, in which said at least two elementary cells (10a, 10b and 10c) are distributed around the periphery of the piezoelectric resonator (2) so that the latter, when operating, exerts an excitation of the same amplitude to within 20%, preferably to within 10%, and / or of the same phase, to within 30°, preferably to within 15°.

16. Holding device according to any one of the preceding claims, in which each primary bar (11) has a thickness at least 10 times greater than the amplitude of deformation which it undergoes due to the operation of the piezoelectric resonator (2).

17. Assembly comprising a holding device (1) according to any one of the preceding claims and at least one piezoelectric resonator (2).

18. Power converter comprising an assembly according to the preceding claim.

19. Power converter according to the preceding claim, wherein the piezoelectric resonator (2) is configured to vibrate in at least one of its first vibration modes, for example its transverse vibration mode and / or its longitudinal vibration mode.

20. A power converter according to any one of the two preceding claims, wherein the piezoelectric resonator (2) has a resonant frequency and an antiresonance frequency, different from each other, and is configured to operate between its resonant frequency and its antiresonance frequency.

21. Method for dimensioning a holding device (1) according to any one of claims 1 to 16, comprising: • dimensioning at least one, preferably each, primary bar (11) of at least one, preferably each, elementary cell (10a, 10b, 10c) so that, with a piezoelectric resonator (2) configured to vibrate in a determined frequency band, the primary bar (11) is in resonance, to within 20%, advantageously to within 10%, with the vibrations of the piezoelectric resonator (2) for any excitation frequency located in said determined frequency band, and / or • dimensioning at least one, preferably each, of the first and second secondary bars (12 and 13) of at least one, preferably of each, elementary cell (10a, 10b, 10c) so that it has a length substantially equal to a multiple of half a wavelength for a chosen excitation frequency located in the determined frequency band, and preferably at its center or its geometric center, and have, with respect to their longitudinal axis, a quadratic moment at least four times greater, preferably at least ten times greater, than a quadratic moment of the primary bar (11) with respect to its longitudinal axis, and / or dimensioning the tertiary bar (14) of at least one, preferably of each, elementary cell (10a, 10b, 10c), so that it has a length substantially equal to the length of the primary bar (11) of the elementary cell considered, a thickness greater, preferably at least twice greater, than a thickness of the primary bar (11) of the elementary cell considered, and is adapted in mechanical impedance with the first and second secondary bars (12 and 13) of the elementary cell considered.

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