Dynamic response of an elastic medium containing crack

• The motion equation and boundary conditions for dynamic loading of cracks yield DIE.
• Solution of DIE by double Laplace–Hankel transforms and properties of Bessel functions.
• Far from the loading source the wave's amplitude decreases while its period increases.

A fundamental solution for an infinite elastic medium containing a penny-shaped crack subjected to dynamic torsional surface tractions is attempted. A double Laplace–Hankel integral transform with respect to time and space is applied both to motion equation and boundary conditions yielding dual integral equations. The solution of the derived dual integral equations is based on an analytic procedure using theorems of Bessel functions and ordinary differential equations. The dynamic displacements’ field is obtained by inversion of the corresponding Laplace–Hankel transformed variable. Results of a representative example for a crack subjected to pulse surface tractions are obtained and discussed.