On the Irregular Eigenvalues In Wave Radiation Solutions Using Dual Boundary Element Method

Abstract

This paper presents the mechanism for the irregular frequencies appearing in the wave radiation problem using the dual BEM. The relation between the matrices of influence coefficients for interior and exterior acoustic problems is examined. Also, the irregular (fictitious) frequencies (eigenvalues) embedded in the singular or hypersingular integral equations are discussed, respectively. It is found that the irregular values depend on the kernels in the integral representation for the solution. Numerical experiments using dual formulation program are conducted to check the validity in comparison with the theoretical proof of the independence of boundary conditions which have been shown by Chen using the degenerate kernels. A two-dimensional dual BEM program for the exterior acoustic problems was developed. Numerical examples are demonstrated by using the dual BEM program. Two cases, including the exterior Dirichlet and Neumann problems, show that the singular integral equation produces the fictitious eigenvalues which are associated with the eigenfrequencies of interior Dirichlet problem, while the hypersingular integral equation produces the fictitious eigenvalues which are associated with the interior Neumann problem.