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

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Abstract
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.

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