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 | References | Similar Articles | Additional Information

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