Abstract
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.
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