Some analytical results for acoustic scattering through a periodic array of elastic membranes

Scarpetta, Edoardo; Sumbatyan, Mezhlum

doi:10.1090/S0033-569X-07-01064-5

Authors: Edoardo Scarpetta and Mezhlum A. Sumbatyan
Journal: Quart. Appl. Math. 65 (2007), 737-755
MSC (2000): Primary 74K15
DOI: https://doi.org/10.1090/S0033-569X-07-01064-5
Published electronically: October 16, 2007
MathSciNet review: 2370358
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Abstract: In the context of wave propagation through acoustic media, an analytical approach is developed to study the (normal) incidence of a pressure wave into a periodic array of (thin) elastic membranes. The frequency of this wave is assumed in a range implying the so-called one-mode (far field) propagation, so that mild approximations holding in this range can be employed. Thus, the problem is reduced to some integral equations based on the opening between adjacent membranes and independent of the frequency. By means of the (analytical) solutions of such equations, an explicit formula for the transmission coefficient is set up and reflected in some figures for concrete values of the various parameters involved. The peculiarities of the scattering structure are discussed.

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