Torsional impact response of a thick-walled cylinder with a circumferential edge crack

This paper considers the torsional impact response of a long thick-walled cylinder containing an internal or external circumferential edge crack. Laplace and Hankel transforms are used to reduce the elastodynamic problem to a pair of dual integral equations. The dual integral equations are solved by using the standard transform technique, and the result is expressed in terms of an integral equation which has a generalized Cauchy kernel as the dominant part. The kernel of the integral equation is improved in order that the calculation may be made easy. A numerical Laplace inversion technique is used to recover the time dependence of the solution.