Radiation impedance matrix of a rectangular aperture, with arbitrary vibration, in a rigid baffle

Abstract

The present paper shows that multidimensional integrals associated with radiation from a rectangular surface in a plane rigid baffle can be reduced to one-dimensional integrals. If the vibrational excitation is expanded into a summation over a set of basis functions, the surface pressure and velocity may be related by an infinite matrix. Each element of the matrix is expressed as a quadruple integral. The numerical evaluation of such integrals, although possible, is prohibitively time consuming for many practical applications. However, for some choices of the basis functions, each quadruple integral may be reduced analytically to single integrals. Explicit expressions are given for square surfaces and with the basis functions taken as products (or sums of products) of trigonometric functions. Numerical results agree well with previous results published in the literature for the pressure distribution over a surface when the vibration is uniform.