Determination of scattering frequencies for two-dimensional acoustic problems using boundary element method

Haifeng Gao,Toshiro Matsumoto,Xiaolai Qiu,Huidong Xu,Changjun Zheng

doi:10.1177/1461348419879604

Abstract

This paper presents a numerical approach for the determination of scattering frequencies of two-dimensional acoustic exterior resonance problems using boundary element method combined with a contour integral method. Since the solving range is surrounded by a Jordan curve in the complex plane, the complex eigenvalues can be acquired through evaluating the contour integral along the Jordan curve using the contour integral method. Complex scattering frequencies are directly extracted by the proposed approach, and their corresponding eigenmodes are also presented by evaluating the vibration amplitudes of internal points. The behaviors of the fictitious eigenfrequencies for unbounded domain are also studied. Numerical examples demonstrate the effectiveness of the approach for the resonance problems of unbounded domains.

Highlights

When an incident wave is propagating through the interfaces of two different mediums or encounter a rigid obstacle as shown in Figure 1, the maximum amplitude of the scattering wave can be excited at the real frequencies located in the vicinity of the scattering frequencies
Some results of scattering frequency analysis based on boundary element method (BEM) and block Sakurai-Sugiura method (BSSM) are presented
BSSM is employed to project the eigenspace to relatively reduced small eigenspace and extracts the nonlinear eigenvalues derived by BEM

Summary

Introduction

When an incident wave is propagating through the interfaces of two different mediums or encounter a rigid obstacle as shown in Figure 1, the maximum amplitude of the scattering wave can be excited at the real frequencies located in the vicinity of the scattering frequencies. Boundary elements can be employed to simulate arbitrary geometrical cross-section with both smooth and corrugated surfaces, and the accuracy can be improved by adopting higher order elements For eigenfrequency computations, both interior and exterior problems result in nonlinear eigenvalue problems, since the parameter x (circular frequency) or k (wave number) is involved in the each element of the system matrix from the boundary integral equations. In this paper, the exterior problems result in fictitious solutions as real eigenfrequencies and the desired scattering frequencies are usually complex numbers. The singular values corresponding to those eigenfrequencies near the Jordan curve do not separate rapidly with the increasing of N These results can be filtered out and artificially by using the defined solving region

Findings

Discussion

Conclusion