Pulse scattering by baffled cavity‐backed membranes

Abstract

A flexible membrane backed by a rigid cavity is set into an infinite plane baffle. The membrane lies in the plane, and the cavity is in the lower half‐space. The upper half‐space contains a homogeneous acoustic fluid. The cavity is filled with another homogeneous acoustic fluid. A pulse, which satisfies the acoustic wave equation in the upper half‐space, is incident on this baffled membrane. Asymptotic expansions as ε→0 that are uniformly valid in t are obtained for the membrane’s motion and the scattered and cavity acoustic fields. Here, ε≪1 is the ratio of the density of the fluid in the upper half‐space to the membrane’s density. If the bandwidth of the pulse’s spectrum is sufficiently narrow, so that it is free of any of the resonant (natural) frequencies of the membrane or of the cavity, then the pulse is essentially reflected as though the baffled, cavity‐backed membrane is rigid. However, if the pulse’s spectrum is sufficiently broad, so that it contains cavity and membrane resonant frequencies, an additional scattered field is produced by its interaction with the membrane’s motion and the acoustic field inside the cavity. This scattered field insonifies distant observation points after the rigidly reflected pulse arrives. It is a complicated sum of slightly damped and oscillating outgoing spherical waves. The damping occurs on the two time scales εt and ε2t. Some of these damped spherical waves are perturbations, due to the cavity fluid, of the ‘‘decayed ringing’’ of the vacuum‐backed, baffled membrane. Application is given to the circular membrane that is backed by a cylindrical cavity, of the same radius as the membrane, and insonified by the normally incident, plane, spiked pulse. Graphs of the membranes motion are presented.