Evaluated Rayleigh integrals for delta‐function driven circular membranes

Abstract

Analytic and semianalytic evaluations of the pressure field due to impulsively driven flat membranes imbedded in an infinite plane baffle by using Rayleigh's integral are discussed and presented for a variety of delta function type motion distributions across the membrane. We first review the field due to a circular membrane subject to a uniform delta function acceleration, and then treat more complex membrane motions composed of different spatially and temporally dependent delta function accelerations. These will include annular (ring) and uniformly expanding annular (moving ring) distributions. In some cases closed analytic forms for the pressure field can be obtained, while in others elliptic integrals result, which can be conveniently calculated by Gauss‐Chebyshev quadrature of the first kind. All evaluations are performed directly in the time domain. [Work performed under auspices of U.S. Department of Energy by LLNL under Contract W‐7405‐Eng‐48.]