Transient torsional vibration of a solid non-homogeneous circular cylinder

This paper is concerned with the solution to the problem of transient torsional vibration of a semi-infinite solid circular cylinder of non-homogeneous material when a torsional shear stress is suddenly applied on the end surface. Solution is obtained by Laplace transform method. Explicit formulae are given for the particle displacement and velocity and stresses in the integral form. These formulae are used to compute the particle velocity and displacement for particular type of stress distribution throughout the end surface.