Quarterly of Applied Mathematics

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

Author(s): Edoardo Scarpetta; Mezhlum A. Sumbatyan
Journal: Quart. Appl. Math. 65 (2007), 737-755.
MSC (2000): Primary 74K15
Posted: October 16, 2007
MathSciNet review: 2370358
Retrieve article in: PDF

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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