ATILA Code Research Articles

Numerical and experimental study of radiated fields of high-power ultrasonic transducers for industrial applications in gases

Flexural axisymmetric vibrating plates with an extensive surface and stepped profile have been shown to be very useful high-power ultrasonic radiators. In fact, the stepped profile provides a highly directional or focused radiation which makes them highly efficient for gases and interphase applications. In this work we present a numerical–experimental study of the displacement distribution and the radiated field of various transducers (directional and focusing transducers working at different frequencies). The numerical model is based on a mixed finite element-boundary element method. The method basically consists of calculating the distribution of displacements of the transducers by the finite element method by using the code ATILA while the corresponding radiated field is calculated by the boundary element method by means of the code EQI. The influence of the loading medium on the displacement distribution is also calculated by the boundary element method. In this way the near and far field of the transducers is calculated as well as their directivity pattern and vibration distribution. The results obtained are compared with experimental data.

Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method

The finite element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single or doubly periodic passive structures [A. C. Hladky-Hennion et al., J. Acoust. Soc. Am. 90, 3356–3367 (1991)]. This paper presents a new extension of this technique to the analysis of the propagation of plane acoustic waves in passive periodic materials without losses and describes with particular emphasis its application to doubly periodic materials containing different types of inclusions. In the proposed approach, only the unit cell of the periodic material has to be meshed, thanks to Bloch–Floquet relations. The modeling of these materials provides dispersion curves from which results of physical interest can be easily extracted: identification of propagation modes, cutoff frequencies, passbands, stopbands, as well as effective homogeneous properties. In this paper, the general method is first described, and particularly the aspects related to the periodicity. Then a test example is given for which analytical results exist. This example is followed by detailed presentations of finite element results, in the case of periodic materials containing inclusions or cylindrical pores. The homogenized properties of porous materials are determined with the help of an anisotropic model, in the large wavelength limit. A validation has been carried out with periodically perforated plates, the resonance frequencies of which have been measured. The efficiency and the versatility of the method is thus clearly demonstrated.

Coupling finite element and boundary element methods on a mixed solid–fluid/fluid–fluid boundary for radiation or scattering problems

The coupling between the finite-element and boundary-element methods is presented in which part of the coupling surface is a solid–fluid interface and part a fluid–fluid interface. The equations are derived for the case of quadratic elements on the finite-element side (atila code) and surfaces of uniform velocity on the boundary-element side (chief code). The accuracy of the method is illustrated by two examples: the scattering of plane waves from a fluid sphere and from a spherical Helmholtz resonator.

Coupling finite element and impedance element to model the radiation of piezoelectric transducers in boreholes

In the context of petroleum acoustics, it is of great interest to modelize the radiation of the piezoelectric transducer in a borehole surrounded by an homogeneous isotropic elastic formation of infinite extent without restrictive assumptions on the geometry, radiation pattern, or types of waves. The finite element method is well suited to solve such problems if the troncature of the infinite formation is correctly treated. This troncature generates ingoing waves which normally do not exist in infinite domain. In this paper, classical finite elements (atila code) are used to model in steady state the transducer, the fluid-filled borehole, and part of the formation inside a spherical boundary. On this exterior boundary, impedance elements are used to take into account the infinite character of the formation. These elements are obtained by discretizing the mechanical impedance of outgoing spherical P and S waves. The method is validated by studying two configurations having analytical solutions: the pulsating sphere and the oscillating point. Results include displacement fields and radiation patterns for P or/and S waves. Finally, the radiation of a cylindrical piezoelectric transducer in an oil-filled borehole [S. Kostek etal., J. Acoust. Soc. Am. 95, 109 (1994)] is analyzed. P and S components of the displacement field, electrical admittance of the transducer, directivity patterns, and distribution of radiated energy are displayed.

Application of the T-matrix method to the numerical modeling of an array of active acoustic transducers

The conventional T-matrix method is a procedure for the computation of the far-field scattering of a plane wave by a compact but otherwise arbitrary collection of scatterers [cf. V. V. Varadan and V. K. Varadan, J. Acoust. Soc. Am. 70, 213–217 (1981)]. Its strength is that the effects of multiple scattering to all orders are rigorously and self-consistently obtained from the single-scattering properties of each scatterer in a free-field environment. For acoustic waves, the T-matrix method has been extended to the case where the source of the scattered radiation is the scatterers themselves, i.e., to the case of an array of active transducers. As an example, the method has been applied to an array of piezoelectric spherical shell sonar transducers. A description of the T-matrix method applied to active acoustic arrays will be given. The use of the finite-element code ATILA [J. N. Decarpigny etal., J. Acoust. Soc. Am. 78, 1499–1507 (1985)] to compute the single-transducer radiation and scattering properties will be described. Results will be compared to Pritchard’s approximation. [Work sponsored in part by the Naval Postgraduate School and the Naval Undersea Warfare Center.]

Modélisation du transducteur BF "Janus-Helmholtz". Nouvelle interprétation du fonctionnement et application à la tomographie acoustique de l'océan

Ocean Acoustic Tomography (measurement of the dynamic behaviour of the ocean) has needs for low frequency, high efficiency, broadband and great depth transducers, in order to reach ranges above 500 km [1]. The double-ended longitudinal «Janus-Helmoltz» projector designed by DCN INGENIERIE SUD widely answers these requirements. An attractive characteristic of such a transducer is the coupling between two resonances implying a large bandwidth.The first observed resonance is usually interpreted as a Helmholtz resonance and the second one as the driver resonance. First part of this study is about the working principles of the Janus-Helmholtz source. Two modelling tools have been used: the finite-element code ATILA and an equivalent circuit model. Thanks to them, a new interpretation of each resonance has been obtained and this transducer has then been optimized for acoustic tomography

Electromechanical coupling coefficients and far-field radiation patterns of lithium niobate bars (Y-cut) used in high-frequency acoustical imaging and nondestructive testing

For high-frequency applications in ultrasonic imaging and nondestructive testing, lithium niobate (LiNbO3) can be used when cut under the shape of long bars with proper orientation and width to thickness ratio W/T. However, due to a strong material anisotropy, the modeling of such elementary bar transducers, for the sake of optimization, is quite difficult. In this paper, the use of the finite element method, with the help of the ATILA code, is proposed to compute resonance frequencies, coupling coefficients, electrical impedances and in-water far-field directivity patterns. (YZw)36° and (YXl)36° cuts with different W/T ratios have been analyzed and numerical results have been carefully and successfully compared with measurements. Main results concern the (YZw)36° cut for which symmetrical directivity patterns are obtained. In this case, a quite constant value is found for the thickness mode coupling coefficient ke in the ranges W/T<0.8 (ke≊50%) and 1.2<W/T<1.7 (ke≊40%). For the (YXl)36° cut, the directivity pattern is nonsymmetrical. In all the cases, a clear physical interpretation of transducer radiation characteristics is provided in terms of vibration modes. This analysis is the first application of new damping finite elements developed together with a specific extrapolation method and presented in a previous, companion paper [Assaad et al., J. Acoust. Soc. Am. 94, 562–573 (1993)].

Understanding coupling between flexural disk transducers from near field measurement

Both in civilian and military applications of underwater acoustics the need of high‐power, directional low‐frequency sources has stimulated the development of volumetric arrays of closely spaced transducers. Understanding the coupling between transducers in the array becomes fundamental to proper beamforming in the active sonar array. The paper presents the study of two flexural double bilaminar disk transducers by the method of finite elements using the ATILA code. The modification of the vibration behavior and the near‐field radiation distortion of an element induced by an adjacent element are computed. The results are compared with the measurement of the displacement on the flexural disk using surface mounted strain gages and the pressure field near the transducers. [Work supported by the French Delegation Generale pour l’Armement and the Naval Postgraduate School.] a)French Naval Engineer. Permanent address: DCN Toulon/SDET/BP77, Toulon 83000, France.

Finite element modeling of active periodic structures: Application to 1–3 piezocompositesa)

The finite-element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single periodic passive structures, such as compliant tube gratings [A.-C. Hennion et al., J. Acoust. Soc. Am. 87, 1861–1870 (1990)], or by doubly periodic passive structures, such as Alberich anechoic coatings [A.-C. Hladky-Hennion et al., J. Acoust. Soc. Am. 90, 3356–3367 (1991)]. This paper presents an extension of this technique to active periodic structures, and describes with particular emphasis its application to the modeling of 1–3 piezocomposites made of parallel piezoelectric connecting strips in a passive matrix. The method can also be applied to many other piezocomposites or to large high-frequency arrays. In the proposed approach, only the unit cell of the active structure and a small part of the surrounding fluid domain have to be meshed, while the acoustic field on both sides of this mesh is described by a plane-wave expansion including progressive and evanescent contributions. Internal losses and anisotropy of the materials as well as normal or oblique incidence of the impinging wave, if this wave exists, can be taken into account in the model. In this paper, the general method is first described, and particularly the aspects related to the piezoelectric elements. Then, one test example is given, for which analytical results exist. This example is followed by a detailed presentation of finite-element results, which are compared with the corresponding measurements (free-field voltage sensitivity or transmitting voltage response), in the case of a given 1–3 composite. The accuracy of the whole approach is thus clearly demonstrated. Finally, the influence of the geometric parameters of a 1–3 composite is studied, while at the same time the limitations of previously published simple analytical models are discussed.

Application of the finite element method to two-dimensional radiation problems

Acoustic fields radiated by vibrating elastic bodies immersed in an infinite fluid domain are, in general, quite difficult to compute. This paper demonstrates in the two-dimensional (2-D) case that the radiated near field can be easily obtained using the finite element method if dipolar damping elements are attached to the mesh external circular boundary. These elements are specifically designed to absorb completely the first two components of the asymptotic expansion of the radiated field. Then, the paper provides a new extrapolation method to compute far-field pressures from near-field pressures, using the 2-D Helmholtz equation and its solution obeying the Sommerfeld radiation condition. These developments are valid for any radiation problem in 2D. Finally, two test examples are described, the oscillating cylinder of order m and a finite width planar source mounted in a rigid or a soft baffle. This approach is the generalization to 2-D problems of a previously described approach devoted to axisymmetrical and three-dimensional (3-D) problems [R. Bossut et al., J. Acoust. Soc. Am. 86, 1234–1244 (1989)]. It has been implemented in the ATILA code. It is well suited to the modeling of high-frequency transducers for imaging and nondestructive testing.

Analysis of an Ultrasonic Piezoelectric Motor Using Numerical Modeling

Ultrasonic motors use a frictional force, produced by high frequency vibrations created by the piezoelectric effect of the stator, to drive the rotor. These devices have been widely stud ied, especially in Japan. A stator of a piezoelectric ultrasonic rotating motor, which uses Lamb waves vibrations, has been modeled using the finite element code ATILA. It takes into account three-dimensional piezoelectric effects and electrical excitations. ATILA permits the computation of the resonance frequency and the effective coupling coefficient of each vibrational mode, the electrical impedance and the elliptical displacement field. The governing electromechanical coupling has been determined. Con sequently, the selection of active material and stator geometry may be optimized to provide an improved transduction efficiency.

Three-dimensional finite element model of a high-power, low-frequency ring-shell flextensional sonar transducer

A three-dimensional finite element model of a high-power, low-frequency ring-shell flextensional transducer [Sparton of Canada, Ltd., model 34A0610] has been developed for use with the ATILA code [Decarpigny etal., J. Acoust. Soc. Am. 78, 1499–1507 (1985)]. A three-dimensional model is needed to represent nonaxisymmetric vibrations that can occur in a dense sonar array. The model was derived from a two-dimensional axisymmetric model developed by Blottman [J. B. Blottman, Naval Undersea Warfare Center, New London Laboratory, Technical Memorandum No. 89-1090 (1989)]. In extending Blottman’s model to three dimensions, reasonable simplifications were made to minimize the number of elements required to faithfully represent the dynamical behavior of the transducer in the frequency range of interest. A description of the model and the results of in-air modal and in-water harmonic analyses will be presented. [Work sponsored in part by the Naval Postgraduate School and the Naval Undersea Warfare Center.] a) Lieutenant Commander, Brazilian Navy.

Analysis of the scattering of a plane acoustic wave by a doubly periodic structure using the finite element method: Application to Alberich anechoic coatings

The finite element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single periodic structures, such as compliant tube gratings [A. C. Hennion et al., J. Acoust. Soc. Am. 87, 1861–1870 (1990)]. In this paper, the same approach is extended to doubly periodic structures, such as Alberich anechoic coatings. To do this, only the unit cell of the periodic structure, including a small part of the surrounding fluid domain, has to be meshed, due to the use of classical Bloch type relations. Then, the effects of the remaining fluid domain are accounted for by matching the pressure field in the finite element mesh with simple plane-wave expansions of the ingoing and outgoing waves. After an outline of the method, the paper describes the results obtained for the scattering of a plane wave by different periodic structures. Internal losses are taken into account and the incident plane wave impinges at normal or oblique incidence. Numerical results obtained for Alberich anechoic coatings are first analyzed to check the convergence and then compared to previous numerical results or to experimental results, demonstrating that the finite element approach is accurate and well suited to predict the behavior of these gratings. Moreover, careful attention is devoted to the analysis of the inclusion vibrations, to identify the origin of the resonance mechanisms.

Finite element modeling of acoustic transducers.

In recent years, the need for designing piezoelectric or magnetostrictive acoustic transducers with actually three-dimensional geometries and thus exhibiting complex displacement fields has become urgent. This is the case in underwater acoustics, for sonar or oceanographical applications, with the renewed interest in flextensional projectors or various Helmholtz resonators. This is also the case in the field of geophysical exploration, where the specific conditions related to the borehole dimensions and to the harsh environment as well as the use of dipole sources imply the development of specific transducers such as rings or benders. The use of simple models to optimize these types of transducers is difficult, if not impossible. Thus numerical methods such as finite elements or integral equations are needed to reach this goal. The purpose of this paper is first to describe the use of the finite element method to analyze the static, modal, or harmonic behavior of transducers. A brief survey of the theoretical formulation is given while more emphasis is devoted to the modeling conditions. Coupling to integral equations is also discussed. Then, some numerical results obtained for in-air and in-water transducers using the atila code are described and compared with experimental results. Finally, a temperature analysis of the problem related to the modeling of the acoustic wave propagation in the formations is discussed.

Finite element modeling of active periodic structures.

The finite element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single passive periodic structures, such as compliant tube gratings [A.-C. Hennion etal., J. Acoust. Soc. Am. 87, 1861–1870 (1990)], or by doubly passive periodic structures, such as Alberich anechoic coatings [A.-C. Hennion etal., J. Acoust. Soc. Am. Suppl. 1 88, S115 (1990)]. Within this approach, only the unit cell of the structure, including a small part of the surrounding fluid domain, has to be meshed, while the acoustic field on both sides of this mesh is described by a plane wave expansion, with progressive as well as evanescent contributions. Internal losses and anisotropy of the materials as well as normal or oblique incidence of the wave can be described in the model. This technique has been extended to active periodic structures, such as composite piezoelectric materials, parallel piezoelectric connecting strips in a passive matrix, for example, or large high frequency arrays. In this communication, the general method is first presented, particularly the aspects related to the piezoelectric elements. Then, several examples are given, for which analytical models exist. Finally, finite element results are compared with experiments in the case of the free-field voltage sensitivity or the transmitting voltage response of 1–3 piezocomposites and demonstrate the accuracy of the whole approach.

Analysis of mechanical limitations of high power piezoelectric transducers using finite element modelling

The design of high power electro-acoustic transducers is a difficult problem in many fields of acoustics. The mechanical, electrical, thermal or acoustical phenomena which limit the available power need to be controlled. To determine the mechanical limitations of a transducer, knowledge of both the mechanical limit of the materials and the stress field in the structure is essential. Although there are many experimental data available to designers, the classical transducer models are limited to simple geometries. The present study uses the finite element code ATILA to compute the stress field, which is then compared to the mechanical limit of the material using classical criteria. The method has been applied to analysis of the mechanical behaviour of a length expander transducer used in macrosonics, the problem of interest being application of prestress, as well as the dynamic behaviour at high drive levels. In both cases, very good agreement is found when the computed results are compared to strain gauge measurements.

Analysis of the scattering of a plane acoustic wave by a doubly periodic structure using the finite-element method

In an attempt to design low-frequency nonreflecting or nontransmitting coatings for underwater applications, many new heterogeneous multilayer structures have been studied in recent years. In the general case, each layer is homogeneous and more or less complex models can be built using a standard transfer-matrix approach. However, in some cases, one or several constitutive layers contain doubly periodic inclusions, such as spherical or cylindrical cavities, used to enhance energy absorption via resonance effects. Then, the modeling requires a larger effort to take account of this periodicity and of the actual displacement field inside each elementary cell. To do this, a finite-element approach has been set up, using the ATILA code and following the method already developed to analyze wave scattering by compliant tube gratings [A. C. Hennion et al., J. Acoust. Soc. Am. 87, 1861–1870 (1990)]. Within this approach, only the unit cell of the structure, including a small part of the surrounding fluid domain, has to be meshed, while the acoustic field on both sides of this mesh is described by a plane-wave expansion, with progressive, as well as evanescent, contributions. Internal losses and anisotropy of the materials, as well as normal or oblique incidence of the wave, can be described in the model. In this communication, the general method will first be presented. Then, several applications will be given, related to classical Alberich coatings made up with different viscoelastic materials. Finally, comparisons with insertion loss measurements will demonstrate the accuracy of the whole approach. [Work supported by D.R.E.T, Paris.]

New designs of class V flextensional transducers with ATILA

The improvements sought in range and performance of sonar arrays require the use of higher acoustical powers at lower frequencies from radiators of reduced dimensions. At the present time, flextensional transducers seem to offer a good solution. Two kinds of flextensional transducers are generally employed: classes IV and V. In the first case, the motors consist of parallel stacks of ceramics, the shell providing the prestressing. In the second case, the motors are made from ceramics staves arranged to form a ring, the prestressing being achieved by wrapping the ring with glass fibers under tension. However, because it is not conventional, the application of prestress in these two cases remains delicate and imprecise. The purpose of this paper is to analyze by the finite element code ATILA [Decarpigny et al., J. Acoust. Soc. Am. 78, 1499–1507 (1985)] an original idea for a class V flextensional transducer that does not suffer from this disadvantage. This flextensional transducer is made from a segmented ring on which are mounted classical ceramic stacks arranged in the form of an inscribed polygon. Several shell configurations will be modeled and analyzed with a special emphasis on technical advantages of these new flextensional designs.

Hydrophone noise induced by turbulent boundary layer pressure fluctuations

The noise induced by the turbulent boundary layer pressure fluctuations on hydrophones embedded in an elastomer layer is usually predicted by assuming that the layer is unbounded in the lateral direction and the hydrophone does not influence the stress field [S. H. Ko and H. Schloemer, J. Acoust. Soc. Am. 85, 1469–1477 (1989)]. These predictions neglect the flow-induced noise associated with the edges of the layer as well as the diffraction, reflection, or shadowing of the stress field by the hydrophones. To avoid these limitations, the finite element code ATILA [B. Hamonic et al., J. Acoust. Soc. Am. 86, 1245–1253 (1989)] is used to model hydrophones embedded in viscoelastic layers of finite extent. The transfer function of the layer and/or the noise sensed by the hydrophone are computed for a given excitation of the outer surface or of the edges of the layer for different sizes. More complex multilayered structures are also examined. [Work partially supported by the Direction des Recherches Etudes et Techniques.]

Analysis of the scattering of a plane acoustic wave by a periodic elastic structure using the finite element method: Application to compliant tube gratings

A two-dimensional mathematical model has been developed to analyze the scattering of plane acoustic waves from an infinite, uniform, plane grating of compliant tubes. It relies upon the finite element method and uses the atila code [J. N. Decarpigny et al., J. Acoust. Soc. Am. 78, 1499 (1985)]. To do this, only the unit cell of the periodic structure, including a small part of the surrounding fluid domain, has to be meshed, thanks to the Bloch–Floquet theorem, and the effects of the remaining fluid domain are accounted for by matching the pressure field in the finite element mesh with simple plane wave expansions of the ingoing and outgoing waves. This paper describes results obtained for the scattering of a plane wave from different tube gratings, including internal losses, at oblique incidence. Comparing finite element results to analytical or experimental results allows for the validation of the model. Then, various compliant tube gratings are considered to demonstrate the efficiency and versatility of this approach. Finally, the generalization to doubly periodic gratings is emphasized.