Isotropic and selective acoustic electromagnetic transducer with a Lamb mode of interest and method for designing such a transducer

Abstract

A coil (402) with a meandering spiral for a selective acoustic electromagnetic transducer for a Lamb wave propagation mode of interest propagating in a structure, the coil comprising several concentric circular portions (C1, C2, C3) connected by meander-shaped portions (M1, M2), each circular portion (C1, C2, C3) consisting of a winding of several turns, the number of turns and the current direction of each circular portion being dimensioned by minimizing the sensitivity of the coil (402) to a set of Lamb modes excluding the mode of interest. Figure 4b

Description

Title of the invention: Isotropic and selective acoustic electromagnetic transducer with a Lamb mode of interest and method for designing such a transducer

[0001] The invention relates to the field of acoustic electromagnetic transducers also called EM AT (ElectroMagnetic Acoustic Transducer) sensors.

[0002] This type of sensor is used in particular in the field of non-destructive testing and integrated health monitoring by guided waves.

[0003] The invention relates more specifically to an acoustic electromagnetic transducer that is both isotropic and selective to a single mode of propagation of Lamb waves. The invention also relates to a method for designing such a transducer.

[0004] In the field of non-destructive testing and integrated health monitoring by guided waves, there are control algorithms which require the selection of a single mode of propagation of guided waves as well as an isotropy of the sensors.

[0005] More specifically, in thin walls, there are several types of guided wave propagation modes: antisymmetric (A) or symmetric (S) Lamb modes, as well as shear (SH) modes. The invention aims to design a sensor that is selective for a single Lamb mode while remaining insensitive to the other modes (A, S, and SH).

[0006] There is therefore a need to design an acoustic electromagnetic transducer that is isotropic and selective to a given Lamb propagation mode while being insensitive to other propagation modes.

[0007] The state of the art includes solutions which only partially address the aforementioned technical problem and / or which present certain drawbacks.

[0008] Reference [1] describes a first type of transducer made from a meander coil. An example of such a transducer is shown in [Fig. 1]. It consists of a meander coil 101 and a magnet 102 and is positioned on a part to be inspected 103.

[0009] This type of coil 101 is composed of several parallel wires, spaced at half the wavelength of the propagation mode of interest, and with opposite current directions. This solution allows for the selection of only one propagation mode of guided waves (modal selectivity) but does not allow for isotropy. It has the disadvantage of being, on the contrary, highly directional.

[0010] Reference [2] describes a second type of transducer based on the use of a so-called "pancake" coil. An example of this transducer is shown in [Fig. 2]. It consists of two spiral coils 201, 202, each wound in a different plane, the two coils being joined by a via 203. This type of coil consists of a spiral of wires whose turns are very close together so as to form a disk containing a maximum number of wires in an orthoradial direction. This second solution allows for isotropic transmission / reception but does not allow for the selection of a single propagation mode.

[0011] Reference [3] describes a third type of transducer based on a circular meander coil, composed of a set of concentric circles, with two adjacent circles having opposite current directions and a spacing of half a wavelength of the mode of interest. An example of such a coil is shown in [Fig. 3]. In this example, two coils 301, 302 are made on two superimposed layers and connected to each other by means of a via 303.

[0012] This type of coil guarantees good isotropy; however, modal selectivity is less efficient than with the first type of meandering coil. Indeed, the half-wavelength spacing between two adjacent circles is only maintained for a wave propagation direction that is along the axis of the coil radius.

[0013] In this case, a large number of circles must be used to obtain satisfactory modal selectivity, for example up to a diameter of 6.5 wavelengths in reference [3], which leads to space constraints at low frequency (for an aluminium plate 3 mm thick, the wavelength is about 20 mm for the A0 mode at 70 kHz, which implies using a sensor of at least 13 cm in diameter).

[0014] To improve the modal selectivity of the transducer, a judicious choice of magnet geometry can be made to make the sensor more sensitive to certain directions of movement and therefore to certain modes. This is, for example, what is done in publication [3], in which the magnets used are chosen to have a magnetic field with an essentially radial direction in the plate, which makes the sensor more sensitive to mode A0 (the mode of interest in the case of the article) and less sensitive to mode S0.

[0015] Apart from the bulkiness, the second drawback is that this type of sensor is very specific to a guided mode of interest, which also induces a range of environmental conditions in which the sensor has the expected properties, which leads to limitations in an application context for integrated health monitoring.

[0016] Reference [4] describes yet another type of solution which reduces the congestion problem of the previous solution while maintaining good modal selectivity. It is based on a circular meander coil of the type As previously described, a magnetic concentrator was added beneath the magnet. Its geometric properties are digitally optimized to eliminate the sensor's sensitivity to all propagation modes except the one being isolated. A magnetic concentrator is a ferromagnetic component that concentrates and directs the magnetic field.

[0017] As with the previous solution, this sensor is designed for a specific propagation mode and for specific parameters of the instrumented structure, which can vary with environmental conditions and therefore reduces its range of use in an integrated health control context.

[0018] Furthermore, this solution has the drawback that the geometry of the magnetic concentrator cannot be modified once manufactured. Thus, any differences between the numerical optimization results and the experimental realization of the sensor (in particular the appearance of modes intended to be eliminated) cannot be corrected by modifying the concentrator geometry accordingly. Consequently, the numerical simulations must be based on an extremely comprehensive and accurate model, and the sensor's performance cannot be improved if it proves not to be sufficiently representative. Moreover, the sensor's modal selectivity is calculated and therefore applicable only for given structural parameters, which limits its use to a certain range of environmental conditions outside of which these parameters can change and impact the sensor's performance.

[0019] The proposed invention overcomes the drawbacks of the aforementioned prior art solutions by using a sensor comprising a meandering circular coil with several circular sections, each composed of a variable number of turns. The number of turns in each circular section is optimized to make the sensor selective to a given Lamb mode while being insensitive to other modes.

[0020] The invention also proposes a method for designing such a coil which aims to determine the optimal number of turns of each circular portion of the coil.

[0021] The invention has the particular advantage of offering an isotropic sensor with modal selectivity that is compact and whose modal selectivity parameters can be easily adjusted or corrected after design, unlike the solution described in reference [4] which requires an additional component (magnetic concentrator).

[0022] To this end, the invention relates to a meandering spiral coil for a selective acoustic electromagnetic transducer with a Lamb wave propagation mode of interest propagating in a structure, the coil comprising several concentric circular portions connected by meander-shaped portions, each circular portion being made up of a winding of several turns, the number of turns and the direction of current of each circular portion being dimensioned by minimizing the sensitivity of the coil to a set of Lamb modes excluding the mode of interest.

[0023] According to a particular aspect of the invention, the circular portions have diameters substantially equal to (k+l)X / 2 where X is the wavelength of the mode of interest and k is a positive or zero integer.

[0024] According to a particular aspect of the invention, the coils of a circular portion are superimposed on each other.

[0025] According to a particular aspect of the invention, the number of turns is different for each circular portion.

[0026] According to a particular aspect of the invention, the number of circular portions is at least equal to a specified number of Lamb wave propagation modes.

[0027] The invention also relates to a selective acoustic electromagnetic transducer with a Lamb mode of interest, comprising a magnet with circular geometry and a coil spiraled in meanders according to the invention.

[0028] According to a particular aspect of the invention, the acoustic electromagnetic transducer comprises a magnetostrictive patch.

[0029] The invention also relates to a method for designing a coil for a selective acoustic electromagnetic transducer with a Lamb mode of interest, the coil being spirally wound in meanders and comprising several concentric circular portions connected by meander-shaped portions, each circular portion being made up of a winding of several turns, the method comprising the steps of: - Choose the number of circular portions, - Determine the sensitivity of each circular portion of the coil to several respective Lamb wave propagation modes, - Define a cost function dependent on a linear combination of the sensitivities of each circular portion to a set of Lamb wave propagation modes excluding the Lamb mode of interest, - Find the values ​​of the coefficients of the linear combination that minimize the cost function, - Determine the number of turns in each circular portion of the spiral coil as being proportional to the absolute values ​​of said coefficients, and the direction of current in each of the circular portions as a function of the signs of said coefficients. - Design the said spiral coil in a meandering pattern

[0030] According to a particular aspect of the invention, the cost function depends on the sum, over the set of Lamb wave propagation modes excluding the Lamb mode of interest, of the modulus or the squared modulus of the sum of the sensitivities of each circular portion, weighted by the coefficients of the linear combination.

[0031] According to a particular aspect of the invention, the sensitivities are determined for several frequency values ​​in a given frequency range and the cost function is equal to the double sum over the set of Lamb wave propagation modes excluding the Lamb mode of interest and over the set of frequencies, of the magnitude or the squared magnitude of the sum of the sensitivities of each circular portion, weighted by the coefficients of the linear combination.

[0032] According to a particular aspect of the invention, the cost function is divided by the modulus or the squared modulus of the sum of the sensitivities to the Lamb mode of interest, of each circular portion, weighted by the coefficients of the linear combination.

[0033] According to a particular aspect of the invention, the sensitivities are determined for several frequency values ​​in a given frequency range and said modulus or squared modulus of the sum of the sensitivities is integrated over said frequency range.

[0034] According to a particular aspect of the invention, the sensitivity of each of the circular portions is determined analytically via a formula depending at least on the radius of the circular portion, the components of the propagation mode, its wavelength and the components of the magnetic field to which the circular portion is subjected or by simulation.

[0035] According to a particular aspect of the invention, the sensitivity of each of the circular portions is determined experimentally by means of the following steps: - Design a first acoustic electromagnetic transducer comprising a circular geometry magnet and a meandering spiral coil comprising several concentric circular portions connected by meander-shaped portions, each circular portion consisting of a winding of one or more turns, each turn of each circular portion being able to be disconnected from the other turns, - For each circular section of the coil, disconnect at least one turn of said circular section from the coil. - To perform a guided wave measurement using the aforementioned circular portion, - For each of the aforementioned Lamb wave propagation modes, isolate the propagation mode on the measurement and determine the sensitivity of the circular portion of said propagation mode from the isolated portion of the measurement.

[0036] According to a particular aspect of the invention, guided wave measurement is carried out by: - positioning the first transducer and a second transducer on a sample, the second transducer being positioned at a predetermined distance from the first transducer as a function of the group velocity of at least one of said propagation modes, - Measuring the guided wave emitted by the second transducer and propagated in the sample.

[0037] According to a particular aspect of the invention, guided wave measurement is carried out by: - positioning the first transducer and a second transducer on a sample, the second transducer being configured to selectively emit one of said propagation modes, - Measuring the guided wave emitted by the second transducer and propagated in the sample.

[0038] In one embodiment, the method according to the invention further includes the search for the diameters of the circular portions and the values ​​of the coefficients of the linear combination which jointly minimize the cost function.

[0039] Other features and advantages of the present invention will become more apparent from the following description in relation to the following accompanying drawings.

[0040] [Fig. 1] represents a diagram of a transducer comprising a meander coil according to the prior art,

[0041] [Fig.2] represents a diagram of a spiral coil according to the prior art,

[0042] [Fig.3] represents a diagram of a circular meander coil according to the prior art,

[0043] [Fig.4a] represents a diagram of an acoustic electromagnetic transducer according to an embodiment of the invention,

[0044] [Fig.4b] represents a diagram of a coil spiraled in meanders according to an embodiment of the invention,

[0045] [Fig.5] represents a flowchart of a method for designing a meandering spiral coil according to an embodiment of the invention,

[0046] [Fig.6a] represents a temporal measurement of an ultrasonic wave by means of a sensor comprising a coil including a circular portion of a first diameter,

[0047] [Fig.6b] represents a temporal measurement of an ultrasonic wave by means of a sensor comprising a coil including a circular portion of a second diameter,

[0048] [Fig.7] represents a diagram showing a signal resulting from an optimized combination of the signals in Figures 6a and 6b to obtain a selective coil for a given propagation mode,

[0049] Figure 4a shows a schematic diagram of an acoustic electromagnetic transducer 400 according to an embodiment of the invention. The transducer comprises a magnet 401 of circular geometry coupled to a meandering spiral coil 402 positioned opposite the magnet.

[0050] The coil 402 is shown in top view in [Fig. 4b]. It consists of several concentric circular portions Ci, C2, C3 (three in the example in [Fig. 4b]) connected together by meandering portions MbM2. Just as in the example in [Fig. 3], the current propagates in opposite directions in two adjacent circular portions (for example between Ci and C2 or between C2 and C3).

[0051] Without departing from the scope of the invention, the meandering portions and the windings of turns can also be arranged so that the current propagates in identical directions between two adjacent circular portions.

[0052] Unlike the coil described in [Fig.3], the coil 402 according to the invention has several turns for each circular portion.

[0053] Advantageously, the number of turns of each portion is different and is optimized so that the transducer 400 is sensitive to a Lamb mode of interest and insensitive to other propagation modes.

[0054] Thus, in the example of [Fig.4b], the first circular portion Ci comprises three turns, the second circular portion C2 comprises five turns and the third circular portion C3 comprises six turns.

[0055] The number of turns shown in [Fig. 4b] is only an illustrative and non-limiting example. This number is determined by optimization so that the coil 402 as a whole is selectively sensitive to a single Lamb wave propagation mode and is as insensitive as possible to other modes.

[0056] The current direction of the circular portions shown in [Fig. 4b] is only an illustrative and non-limiting example. This direction is determined jointly with the optimization of the number of turns.

[0057] Advantageously, the turns of the same circular portion are formed in the same plane with the smallest possible inter-turn spacing. Alternatively, the turns are formed in several superimposed planes, for example they are printed on several layers of dielectric material such as Kapton and are connected to each other by vias passing through the layers.

[0058] According to one embodiment, the circular portions Ci, C2, C3 have an average diameter equal to (k + 1 / 2)A, where 2 is the wavelength of the wave for the propagation mode of interest and the operating frequency, and k is a positive or zero integer. In the case of a frequency range of interest, the wavelength is calculated at the center frequency of the range.

[0059] According to another embodiment, the diameter of the circular portions has an arbitrary value which is optimized jointly with the number of turns of each portion to obtain a modal selectivity of a propagation mode of interest.

[0060] The transducer 400 thus produced is isotropic due to its circular geometry. It is insensitive to the shear propagation modes SH0, SH1,... due to the circular symmetry of the coil and the magnet.

[0061] In the case where the structure to be inspected is not in a conductive material, a magnetostrictive patch is positioned between the transducer coil and the structure.

[0062] A method for designing the meandering spiral coil 402 of [Fig.4b] is now described so as to make the transducer 400 sensitive to a single Lamb wave propagation mode, for example an antisymmetric A mode or a symmetric S mode. In particular, the method aims to determine the optimal number of turns of each circular portion of the coil.

[0063] The method begins at step 500 with the selection of the number of circular segments of the coil. The number of circular segments N is chosen to be at least equal to the total number of Lamb wave propagation modes in the structure to be inspected, and according to the target frequency range. For example, for low-frequency operation, only the guided modes A0, S0, and SH0 exist; therefore, the minimum number of circular segments is two in order to make the coil sensitive to one of the two modes A0 and S0 and insensitive to the other. Due to its circular symmetry, the coil is naturally insensitive to the shear mode SH0.

[0064] In step 501, for each of the circular portions, its sensitivity to each mode of propagation of Lamb waves likely to be present is then determined as a function of the frequency range and the structure to be inspected.

[0065] The sensitivity of each circular portion is determined by considering a single turn per circular portion or by considering several turns per circular portion and then dividing the sensitivity obtained by the number of turns.

[0066] Several methods are possible for estimating the sensitivity of a turn to a Lamb mode. For this, each turn or each circular portion is considered disconnected from the other portions.

[0067] A first variant of the embodiment of step 501 consists of determining the sensitivity analytically, for example by calculating beforehand the Lamb modes existing in the wall of the structure that one wishes to inspect and in the range of frequencies of interest.

[0068] The following formula can be used based on a model where the eddy currents and ferromagnetic effects (in the case where the material of the structure is ferromagnetic) created by the passage of current in the coil are concentrated linearly below it, on the surface of the wall of the structure at ~ =0 (skin effect).

[0069] Ekm ( / )=«[ O ( °> f ) Br ( Rk- 0 ) ( o, f ) B- ( Rk, 0 ) COS0 ] Ad $ ] (1 ) = ^4^(0, / )^(^0) it^f / W^O) / ,(5¾)]

[0070] Ekm(f) is the sensitivity of a circular portion indexed by & to a Lamb mode of index m and to a frequency / . [""11 eiUf'(zf) are 'cs components respectively longitudinal and normal mode of propagation m,

[0072] hm( f ) is the wavelength at the given frequency, Rk the radius of the circular portion (for example Rk = (^+ l / 2)2m( / ) ),

[0073] 6 denotes an integration variable that describes the portion of the coil that is integrated in equation (1).

[0074] Br ( r, z ) and Bz ( r, z ) are respectively the radial and normal components of the magnetic field of the magnet, Jn are the Bessel functions of the first kind, and a is a predefined constant depending on the height of the coil.

[0075] Without departing from the scope of the invention, any other model for calculating the sensitivity of a circular portion of a coil to a Lamb wave propagation mode may be considered.

[0076] A second embodiment of step 501 consists of determining the sensitivity by numerical simulation, for example using multi-physics simulation software that takes into account all electromagnetic (eddy currents, ferromagnetism) and mechanical (wave propagation) phenomena. The sensitivity of each circular portion for each mode at a given frequency is then defined as the complex ratio (amplitude and phase shift) between the signal in the circular portion of the coil and the amplitude of the mode.

[0077] A third alternative embodiment of step 501 consists of determining the sensitivity by experimental measurements.

[0078] Two sub-variants are also conceivable for determining sensitivity by experimental measurements.

[0079] First, a coil of the type described in [Fig. 4b] is required, each circular portion of which must be independently accessible. Each circular portion may consist of a single turn or any number of turns. In other words, the circular portion whose sensitivity is to be calculated is disconnected from the rest of the coil, and its ends are connected to a measuring device.

[0080] A first measurement sub-variant consists of using a first transducer comprising the aforementioned coil operating in reception and a second conventional transducer operating in transmission. The second transducer is used to emit a guided Lamb wave in a chosen structure, and the first transducer is used to measure the wave, after its propagation in the structure, independently through each of the circular portions.

[0081] It is then necessary to separate the different Lamb modes, which are indistinguishable to the same extent. One solution for this is to take advantage of the difference in group velocity or energy velocity between the Lamb modes, which makes it possible to separate the wave packets between the different propagation modes in the time domain. This solution requires a propagation structure large enough to ensure a sufficient distance between the two transducers relative to the group velocity (or energy velocity) of the modes, so as to prevent the first reflections of the faster modes from mixing with the direct paths of the slower modes.

[0082] A second sub-variant consists of using as a second transducer, a sensor capable of selectively emitting each of the modes, alone.

[0083] In the case where the instrumented wall is flat and homogeneous (or with planar symmetry) and the frequency range of interest is small enough that only the Lamb modes A0 and S0 exist, for example, the use in phase or in opposite phase of two piezoelectric pellets glued on either side of the wall is sufficient to separate these two modes.

[0084] Otherwise, selective actuators such as a state-of-the-art EMAT meander coil sensor can be used.

[0085] The sensitivity to be estimated Ekm(f) is that of the circle containing only one turn, but it is possible to carry out measurements with several turns (in order to have a low noise signal) and then divide the result obtained by the number of turns used.

[0086] Sensitivity is, for example, estimated directly by selecting a wave packet over a time measurement and calculating the signal energy in the selected time window. The integral of the square of the signal is calculated over the corresponding time window.

[0087] In step 502, a cost function is then determined from a linear combination of the sensitivities calculated in step 501. The cost function is characteristic of the overall sensitivity of the coil to propagation modes other than the mode of interest.

[0088] It depends on linear combinations of the sensitivities calculated for each circular portion vN rr where Ekm(f) is the sensitivity, calculated in step 501, of the

[0089]

[0090] Circular portion with index k, for the propagation mode with index m and as a function of the frequency f. m varies over the set of so-called "parasitic" modes Mpar, that is, all modes except the mode of interest m0 for which we want the coil to be sensitive. N is the number of circular portions. (¾ ■ • •, are coefficients that are proportional to the number of turns of a circular portion and whose sign is defined by the direction of the current in said portion. For example, the cost function is equal to |2 if the sensitivities are calculated for .^,1^,^.( / )1 a single frequency or

[0091] Q(C. by. if the sensitivities are calculated f I 2 J 1^^( / )1 d / mm

[0092]

[0093] for a frequency range [ / , ; / m,ix] Alternatively, the cost function is taken equal to Q(ch

[0094]

[0095]

[0096]

[0097] mo is the mode of interest. Similarly, the cost function can be taken as equal to - ( C1' • • ■ ' CN ) — par. | ^k- fk^km ( / ) | Or: J max QneW par. I ^k= km ( f ) | J min

[0098] Or:

[0099]

[0100] Without departing from the scope of the invention, the above cost function examples can be replaced by any other cost function that allows the sensitivity of the coil to parasitic propagation modes to be characterized. Step 502 then consists of minimizing the cost function Q to determine the coefficients (cP ---,¾) which allow us to obtain an average sensitivity to all parasitic modes that is as close as possible to 0.

[0101] To ensure a good numerical resolution of this optimization, advantageously, the value of the first coefficient is fixed, for example, equal to = 1.

[0102] In step 503, the number of turns of each circular portion is then determined as being proportional to the coefficient obtained for said portion, and the direction of current of this circular portion as a function of the sign of this coefficient.

[0103] For example, if the numerical optimization of the cost function returns the coefficients (1, 2, -0.5), the number of turns in the three circular portions can be taken to be 100, 200, and 50, or 50, 100, and 25, with the current direction being clockwise, clockwise, and counterclockwise, for example. Variations in the total number of turns induce a variation in the overall sensitivity of the sensor, but not in its modal selectivity. The number of turns affects the sensitivity of the sensor, with this sensitivity generally increasing with the number of turns.

[0104] In step 504, the coil is designed with the number of circular portions, the direction of current and the number of turns of each portion as determined in step 503.

[0105] According to a particular embodiment of the invention, once the coil has been designed, a modal selectivity verification phase is carried out by experimental measurements. If the results obtained do not meet expectations, steps 501 to 503 of the design method are executed again in one or more iterations until the optimum is reached.

[0106] Differences between the initially estimated results and the results actually obtained with the coil once designed may be due to the fact that adding turns to the different circular portions slightly modifies their geometry and therefore their sensitivity. In particular, the approximation that the sensitivity of a circle containing n turns is equal to n times the sensitivity of a single turn is only valid if the n turns are precisely superimposed, that is, if they all have the same radius. Conversely, if the turns are positioned in the same plane, even with a very small inter-turn spacing, each turn will have a slightly different radius from the others, which leads to slight differences between the estimated sensitivities and those obtained with the coil once designed.

[0107] A particular embodiment of the invention applied to the inspection of a 3 mm thick aluminum plate structure measuring 120 by 120 cm is now described. The frequency range of interest is below 100 kHz, a range for which only three guided modes exist in the plate: A0, S0, and SH0. The mode of interest that is to be isolated in this example is A0, with an X wavelength of 20 mm. The EM AT sensors developed consist of a coil comprising two circles with radii of 30 mm (3ÀZ2) and 50 mm (5ÀZ2), respectively, printed in six layers on a Kapton sheet, and a cylindrical neodymium magnet with a diameter of 60 mm and a height of 20 mm. The connectors of Kapton sheets are designed so that each of the six layers can be connected, corresponding to each turn of a circle. The sensor is used for reception. For transmission, a piezoelectric transducer is used to generate the waves. This transducer is excited by a 3-cycle signal at 50 kHz with a Hann windowing pattern.

[0108] To perform step 501, the six layers of each circle are connected in series to increase the sensitivity of each circle, but the circles are not connected to each other. Acquisitions are made for the inner and outer circles, shown in Figures 6a and 6b. At the beginning of the measurement, between approximately 0.05 ms and 0.3 ms, three wave packets are clearly visible. The first, 601,611, corresponds to the first packet of mode S0 (direct path from the piezoelectric transducer to the EMAT), the second, 602,612, to the first packet of mode A0 (also direct path), and the third, 603,613, to the first reflection of mode S0 (the group velocity of mode S0 is approximately three times greater than that of mode A0 in this example). This temporal separation, achieved through a judicious choice of the position of the two sensors, allows the separation of the two modes A0 and S0.As a reminder, the EMAT sensor is not at all sensitive to SH0 mode, due to its circular symmetry.

[0109] For the implementation of step 502, the energy of the signal of the parasitic modes, which are here the S0 modes, divided by the energy of the signal of the mode of interest A0, is used as the cost function. The calculation is carried out on the corresponding time windows.

[0110] The cost function is therefore nz ■. c v(Cj, C2) - C]E1Ai;K-2E2Ao

[0111] Numerical optimization gives the coefficients c( = 1 and c2 = -0.39

[0112] Fig. 7 represents a signal obtained by linear combination of the signals of figures 6a and 6b with the coefficients determined above.

[0113] It is observed that the wave packets of the selected mode A0 (zone 702) are well preserved while those of the parasitic modes (mode S0 zone 701 and zone 703) are strongly attenuated.

[0114] Modal selectivity is not perfect, however, since the signal in zone 703 is not zero. This can be explained by the small number of circles used despite the large bandwidth of the signal.

[0115] We then carry out an implementation of the coil by fixing the number of turns of the inner circle to 5 and the number of turns of the outer circle to 2, which corresponds to a number proportional to the coefficients (1,-0.4).

[0116] In one embodiment of the invention, the diameters of the various circular portions are optimized in conjunction with the number of turns. To this end, the sensitivities (step 501) are determined analytically or by simulation as a function of the diameters. In particular, the diameter values ​​may differ from (k + 1 / 2)X-

[0117] In another embodiment of the invention, the magnet associated with the coil is chosen to promote the modal selectivity of certain guided modes. For example, choosing a cylindrical magnet with a diameter larger than that of the coil results in a magnetic field at the surface of the direction plate that is primarily normal, and therefore sensitive to displacements in the plane, and thus more so to the S0 mode than to the AO mode.

[0118] To favor sensitivity to A modes rather than S modes, a radial magnetic field (i.e. in the plane) should be favored, for example by using a small cylindrical magnet and a larger toroidal magnet as is done in article [3].

[0119] Another variant involves using a magnetic concentrator to maximize the magnetic field strength in the vicinity of the coil wires. This increases the overall sensitivity of the sensor.

[0120] The design method can be computer-aided. It can be implemented as a computer program. References

[0121] [1] “Directivity analysis of meander-line coil EMATs with a purely analytical method”, Yuedong Xie et al, Ultrasonics, vol 73, Jan 2017, p 262-270

[0122] [2] “The excitation and detection of Lamb Waves with planar coil electromagnetic acoustic transducers", Paul D. Wilcox et al, IEEE Transactions on ultrasonics, ferroelectrics, and frequency control, vol 52, n°12, Dec 2005

[0123] [3] “Development of omnidirectional A0 EMAT mode employing a concentric permanent magnet pairs with opposite polarity for plate inspection”, Zenghua Liu et al, NDT& E International, vol 94, Tuesday 2018, p 13-21

[0124] [4] “Development of an omni-directional magnetic-concentrator-type electromagnetic acoustic transducer », Zenghua Liu et al, NDT& E International, vol 109, Jan 2020,

Claims

Demands

1. A coil (402) spirally wound in a meander pattern for an acoustic electromagnetic transducer selective to a Lamb wave propagation mode of interest propagating in a structure, the coil comprising several concentric circular portions (Ci,C2,C3) connected by meander-shaped portions (MbM2), each circular portion (Ci,C2,C3) being made up of a winding of several turns, the number of turns and the current direction of each circular portion being dimensioned by minimizing the sensitivity of the coil (402) to a set of Lamb modes excluding the mode of interest.

2. Coil according to claim 1 in which the circular portions (Ci, C2, C3) have diameters substantially equal to (k+l)X / 2 where X is the wavelength of the mode of interest and k is a positive or zero integer.

3. Coil according to any one of the preceding claims wherein the turns of a circular portion are superimposed on each other.

4. Coil according to any one of the preceding claims wherein the number of turns is different for each circular portion.

5. Coil according to any one of the preceding claims wherein the number of circular portions is at least equal to a specified number of Lamb wave propagation modes.

6. Selective acoustic electromagnetic transducer (400) with a Lamb mode of interest, comprising a circular geometry magnet (401) and a coil (402) spiraled in meanders according to any one of the preceding claims.

7. Acoustic electromagnetic transducer according to any one of the preceding claims comprising a magnetostrictive patch.

8. A method for designing a coil (402) for a selective Lamb mode acoustic electromagnetic transducer (400) of interest, the coil being meander-wound and comprising several concentric circular portions connected by meander-shaped portions, each circular portion being made up of a winding of several turns, the method comprising the steps of: - Choose (500) the number of circular sections, - Determine (501) the sensitivity of each circular section of the coil to several respective Lamb wave propagation modes, - Define a cost function depending on a linear combination of the sensitivities of each circular section to a set of Lamb wave propagation modes excluding the Lamb mode of interest, - Find (502) the values ​​of the coefficients of the linear combination that minimize the cost function, - Determine (503) the number of turns of each circular section of the spiral coil as being proportional to the absolute values ​​of said coefficients and the current direction of each of the circular sections as a function of the signs of said coefficients, - Design (504) said meandering spiral coil

9. A method of designing a coil according to claim 8 wherein the cost function depends on the sum, over the set of Lamb wave propagation modes excluding the Lamb mode of interest, of the modulus or the squared modulus of the sum of the sensitivities of each circular portion, weighted by the coefficients of the linear combination.

10. A method of designing a coil according to claim 9 wherein the sensitivities are determined for several frequency values ​​in a given frequency range and the cost function is equal to the double sum over all Lamb wave propagation modes excluding the Lamb mode of interest and over all frequencies, of the magnitude or the squared magnitude of the sum of the sensitivities of each circular portion, weighted by the coefficients of the linear combination.

11. A method of designing a coil according to claim 10 wherein the cost function is divided by the modulus or the squared modulus of the sum of the Lamb mode sensitivities of interest, of each circular portion, weighted by the coefficients of the linear combination.

12. A method of designing a coil according to claim 11 wherein the sensitivities are determined for several values ​​of frequencies in a given frequency range and said modulus or modulus squared of the sum of the sensitivities is integrated over said frequency range.

13. A method of designing a coil according to any one of claims 8 to 12 wherein the sensitivity of each of the circular portions is determined analytically via a formula depending at least on the radius of the circular portion, the components of the propagation mode, its wavelength and the components of the magnetic field to which the circular portion is subjected or by simulation.

14. A method for designing a coil according to any one of claims 8 to 12, wherein the sensitivity of each of the circular portions is determined experimentally by means of the steps of: - Designing a first acoustic electromagnetic transducer comprising a magnet with circular geometry and a meandering spiral coil comprising several concentric circular portions connected by meander-shaped portions, each circular portion being made up of a winding of one or more turns, each turn of each circular portion being able to be disconnected from the other turns, - For each circular portion of the coil, disconnecting at least one turn of said circular portion from the coil, - Performing a guided wave measurement using said circular portion, - For each of said Lamb wave propagation modes,Isolate the propagation mode in the measurement and determine the sensitivity of the circular portion of said propagation mode from the isolated portion of the measurement.

15. A method of designing a coil according to claim 14 in which the guided wave measurement is carried out by: - ​​positioning the first transducer and a second transducer on a sample, the second transducer being positioned at a predetermined distance from the first transducer as a function of the group velocity of at least one of said propagation modes, - Measuring the guided wave emitted by the second transducer and propagated in the sample.

16. Method of designing a coil according to claim 15 wherein the guided wave measurement is carried out by: - ​​positioning the first transducer and a second transducer on a sample, the second transducer being configured to selectively emit one of said propagation modes, - measuring the guided wave emitted by the second transducer and propagated in the sample.

17. Method of designing a coil according to any one of claims 8 to 12 further comprising finding the diameters of the circular portions and the values ​​of the coefficients of the linear combination which jointly minimize the cost function.

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