ON THE THEORY OF TRANSIENT TORSIONAL WAVE PROPAGATION IN A CIRCULAR CYLINDER

Abstract

A general series solution is derived for the propagation of elastic waves in a circular cylinder when a torsional shear stress is suddenly applied to its end surface. Expressions are given for the resulting particle displacement and velocity, and for the stress components. These expressions are used to compute the particle velocity and stress waves propagated along the surfaces of the cylinder, for an input stress applied to the inner region of the end surface. It is shown that the particle velocity shows fluctuations which do not decay in magnitude as the wave propagates in the axial direction, though their frequency increases. For the particular problem solved numercically, it is found that the maximum particle velocity and stress at the surface of the cylinder are about twice those given by the elementary theory, and that a large number of fluctuations occur before their amplitude decays to a negligible value.