A FOURIER SERIES APPROACH TO THE MEASUREMENT OF FLEXURAL WAVE INTENSITY IN PLATES

Abstract

In regions sufficiently remote from excitation and discontinuities, the flexural motion of a plate can be expressed as the sum of plane propagating waves. In this paper this fact is used as the basis of a wave-based technique for plate intensity measurement. It is assumed that far field conditions exist, and that the displacement within a region can be described as the sum of a set of plane waves the amplitude of which is a function of propagation direction. This function is approximated using a truncated complex Fourier series. It is shown that the time-averaged intensity at the co-ordinate origin can be written in terms of the five Fourier coefficients of lowest order. The effect that the choice of measured variables and measurement locations have on systematic errors and on the conditioning of the problem is discussed. A numerical comparison, under specific conditions, between a Fourier series approach and a finite difference approach to plate intensity measurement is shown. This indicates that the Fourier series approach can offer a better compromise between systematic and random errors. Experimental intensity measurements illustrating the use of the Fourier series approach are presented and discussed.