Diffraction of normal compression waves by a penny-shaped crack in the presence of an axial magnetic field

The problem of diffraction of normally incident compressional waves by a penny-shaped crack located in a perfectly conducting, infinite, isotropic, elastic solid permeated by an uniform magnetostatic field is considered. Using an integral transform technique, the problem is reduced to that of solving a Fredholm integral equation of the second kind having a finite integral kernel. The dynamic singular stress distributions near the crack tip are obtained in closed form and the effects on the dynamic stress-intensity factors due to the presence of the magnetic field are shown graphically. For low frequencies, the dynamic stress-intensity factors are expressed in series of ascending powers of the normalized frequency. The approximate solutions are compared with exact solutions.