Application of the integral equation method to two‐dimensional sound diffraction problems

Abstract

This report is concerned with the numerical calculation of two‐dimensional sound diffraction fields around thin rigid plates by the integral equation method. Generally, the basic equation used in this method is the Helmholtz integral equation. However, if the objects investigated are infinitely thin plates, the basic equation cannot be applied. In such cases, the normal derivative form of the Helmholtz integral formula (NDF for short) is useful [T. Terai, J. Sound Vib. 69(1), 71–100 (1980)]. When the plate is flat and rigid, the equation to be solved is reduced to an integral equation of the first kind by means of NDF. And, as the fundamental solution in two dimensions is not exp(ikr)/r, but is a zero order Hankel function of the first kind, the treatment of singularities is more complicated. The numerical examples treated in this report are problems of an acoustic barrier consisting of several rigid and flat plates. It is shown that the numerical solutions agree with the analytical ones and also with the experimental results.