Abstract
Steady-state solutions are obtained without distinction of stability if a scattering problem by a crack with contact acoustic nonlinearity is solved by means of a harmonic balance-boundary element method. The present article deals with stability analysis for the steady-state solution. The proposed formulation is based on Hill's method, and the stability analysis comes down to an infinite-dimensional nonlinear eigenvalue problem. The infinite-dimensional matrix is truncated, and the eigenvalue problem is solved by means of the Sakurai-Sugiura method. The obtained numerical results are compared to the conventional transient solutions to demonstrate the validity of the proposed method.
