Abstract
This paper presents a perturbation analysis of the excitation problem for an open domain. As a fundamental study, it addresses wave scattering by a crack in a two-dimensional domain to avoid fictitious eigenfrequency issues, which are encountered in a boundary integral equation. The system comprises a homogeneous, isotropic, and linearly elastic half plane containing interior and surface-breaking cracks. The modal amplitude is approximated using the perturbation method with the Taylor expansion around the complex-valued eigenfrequency for the open domain. The eigenfrequency problem for an open domain is solved using boundary element method and Sakurai-Sugiura method, which is one of the nonlinear eigensolvers. Several numerical results demonstrate that the proposed perturbation method approximately evaluates the modal amplitude due to real-valued frequency excitation.
