Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


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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Additional Information

Edoardo Scarpetta
Affiliation: D.I.I.M.A., University of Salerno, 84084 Fisciano (SA), Italy

Mezhlum A. Sumbatyan
Affiliation: Faculty of Mechanics and Mathematics, Rostov State University, 344090 Rostov-on-Don, Russia

DOI: https://doi.org/10.1090/S0033-569X-07-01064-5
Received by editor(s): August 1, 2006
Published electronically: October 16, 2007
Article copyright: © Copyright 2007 Brown University

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