Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary

Abstract

In this paper, the dual integral formulation for the Helmholtz equation used in solving the acoustic modes of a two-dimensional cavity with a degenerate boundary is derived. All the improper integrals for the kernel functions in the dual integral equations are reformulated into regular integrals by integrating by parts and are calculated by means of the Gaussian quadrature rule. The jump properties for the single layer potential, double layer potential and their directional derivatives are examined and the potential distributions are shown. To demonstrate the validity of the present formulation, the acoustic frequencies and acoustic modes of the two-dimensional cavity with an incomplete partition are determined by the developed dual BEM program. Also, the numerical results are compared with those of the ABAQUS program, FEM by Petyt and the dual multiple reciprocity method. Good agreement between the present formulation and measurements by Petyt is also shown.