An analytical solution for the self and mutual radiation resistances of a rectangular plate

Abstract

It is widely accepted that, for an arbitrary acoustic wave number, the radiation resistance of a simply supported rectangular plate has to be calculated through numerical integration. In this study, an analytical solution for the self and mutual radiation resistances is obtained in the form of the power series of the nondimensional acoustic wave number. Unlike the previous analytical or asymptotic solutions, it is not subject to any of the restrictions usually imposed upon the acoustic wave number. A few numerical examples are given simply to verify the solution and elucidate the reliance of the self and mutual radiation resistances on the acoustic wave number and the plate aspect ratio. It is shown that the present formulae are extremely efficient by cutting the CPU time by orders of magnitude in comparison with the traditional numerical integration scheme. This investigation successfully fills the long-existing gap in solutions for the moderate wave numbers that are often of primary concerns in an acoustic analysis.