FINITE-ELEMENT MODELING OF ACTIVE PERIODIC STRUCTURES - APPLICATION TO 1-3 PIEZOCOMPOSITES

The finite-element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single p eriodic passive structures, such as compliant tube gratings [A.-C. Hen nion et al., J. Acoust. Soc. Am. 87, 1861-1870 (1990)], or by doubly p eriodic 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 stru ctures, and describes with particular emphasis its application to the modeling of 1-3 piezocomposites made of parallel piezoelectric connect ing strips in a passive matrix. The method can also be applied to many other piezocomposites or to large high-frequency arrays. In the propo sed approach, only the unit cell of the active structure and a small p art of the surrounding fluid domain have to be meshed, while the acous tic field on both sides of this mesh is described by a plane-wave expa nsion including progressive and evanescent contributions. Internal los ses and anisotropy of the materials as well as normal or oblique incid ence of the impinging wave, if this wave exists, can be taken into acc ount in the model. In this paper, the general method is first describe d, 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 ca se of a given 1-3 composite. The accuracy of the whole approach is thu s clearly demonstrated. Finally, the influence of the geometric parame ters of a 1-3 composite is studied, while at the same time the limitat ions of previously published simple analytical models are discussed.