NATURAL FREQUENCIES OF A PENNY-SHAPED CRACK WITH SPRING BOUNDARY-CONDITION

Natural frequencies of a penny-shaped crack are calculated for the thr ee-dimensional elastic problem. The crack is imbedded in a homogeneous medium and on the crack surface the spring boundary conditions are as sumed. Only the symmetric problem is considered and the complex freque ncies are given as the SEM (singularity expansion method) poles of the symmetric part of the transition (T) matrix. The T matrix is calculat ed with a direct integral equation method leading to integral equation s relating normal stress and displacement on the crack surface. The lo cation of the poles in the complex frequency plane are compared with t he scattering cross-section versus frequency and with Rayleigh surface waves.