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 o r doubly periodic passive structures [A. C. Hladky-Hennion et al., J. Acoust. Sec. Am. 90, 3356-3367 (1991)]. This paper presents a new exte nsion of this technique to the analysis of the propagation of plane ac oustic waves in passive periodic materials without losses and describe s with particular emphasis its application to doubly periodic material s containing different types of inclusions. In the proposed approach, only the unit cell of the periodic material has to be meshed, thanks t o Bloch-Floquet relations. The modeling of these materials provides di spersion curves from which results of physical interest can be easily extracted: identification of propagation modes, cutoff frequencies, pa ssbands, stopbands, as well as effective homogeneous properties. In th is paper, the general method is first described, and particularly the aspects related to the periodicity. Then a test example is given for w hich analytical results exist. This example is followed by detailed pr esentations of finite element results, in the case of periodic materia ls containing inclusions or cylindrical pores. The homogenized propert ies of porous materials are determined with the help of an anisotropic model, in the large wavelength limit. A validation has been carried o ut with periodically perforated plates, the resonance frequencies of w hich have been measured. The efficiency and the versatility of the met hod is thus clearly demonstrated. (C) 1995 Acoustical Society of Ameri ca.