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Some analytical results for acoustic scattering through a periodic array of elastic membranes. (English) Zbl 1153.76056

Summary: 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 (analytical) solutions of such equations, an explicit formula for the transmission coefficient is set up and reflected in some figures for various parameters involved. The peculiarities of the scattering structure are discussed.

MSC:

76Q05 Hydro- and aero-acoustics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K15 Membranes
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References:

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