Acoustic scattering by baffled cavity‐backed membranes

Abstract

A flexible membrane backed by a rigid cavity is set into an infinite plane baffle. The upper half‐space contains an acoustic fluid, and the cavity which lies in the lower half‐space, contains another acoustic fluid. A time harmonic wave in the upper half‐space is incident on the plane. When the frequency of the incident wave is bounded away from the resonant (natural) frequencies of the membrane, and of the acoustic fluid in the cavity, the reaction of the fluid on the cavity‐backed membrane (CBM) is small. However, near a resonant frequency, the fluid–CBM coupling is significant. The method of matched asymptotic expansions is employed to obtain an asymptotic expansion of the scattered field as e→0 that is uniformly valid in the frequency of the incident wave. Here, e≪1 is the ratio of the upper half‐space fluid and membrane densities. Simple and double resonant frequencies are analyzed; but the method is applicable to higher‐order resonant frequencies. The method is applied to the normal incidence of a plane wave on a baffled circular membrane that is backed by a circular cylindrical cavity. It is found that the CBM is a more ‘‘susceptible’’ scatterer than the vacuum‐backed membrane (VBM). In addition, the signature of the CBM differs from the signature of the VBM. For example, the scattered amplitude for the CBM has peaks with bandwidths of O(e2), in addition to the peaks with bandwidths of O(e) corresponding to the membrane resonant frequencies. Moreover, the CBM can have resonant ‘‘packets’’ that are of total bandwidth (e)1/2.