Diffraction of Torsional Waves by a Flat Annular Crack in an Infinite Elastic Medium

The problem of diffraction of normally incident torsional waves by a flat annular crack embedded in an infinite, isotropic, and homogeneous elastic medium is considered. Using an integral transform technique, the problem is reduced to that of solving a singular integral equation. The solution of the singular integral equation is obtained in the form of the product of the series of Chebyshev polynomials of the first kind and their weight functions. Thus the essential feature of the dynamic singular stress field near the crack is preserved and the crack tip dynamic stress-intensity factor is easily evaluated. Numerical calculations are also carried out and the variations of dynamic stress-intensity factors with the normalized frequency for the ratio of the inner radius to the outer one are shown graphically.