A new concept of modal participation factor for numerical instability in the dual BEM for exterior acoustics

Abstract

This paper presents the occurring mechanism why irregular frequencies are imbedded in the exterior acoustics using the dual boundary element method (BEM). The modal participation factor which dominates the numerical instability is derived for continuous and discrete systems. In addition, the irregular (fictitious) frequencies 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. A two-dimensional dual BEM program for the exterior acoustics was developed. Numerical experiments are conducted to verify the concept of modal participation factor.