The Propagation of Shear Wave in a Viscoelastic Rod

Abstract

The impulsive response of a semi-infinite viscoelastic circular rod to impact torsion is analysed by employing the correspondence relation between linear elasticity and linear viscoelasticity. Supposing that the 3-element standard linear solid model can be applied to the behavior of the rod in shear, we study the influence of the loading condition at the struck end, i.e., the radial distribution of shear stress and rise time of the applied torque on the stress or strain-time history. Analyses are done by the Laplace transformation and the numerical inversion of it by the use of the FFT algorithm. The fluctuations of stress or strain caused by waves of high orders are large when the impulsive torque concentrates near the center of the struck end. With increase of the viscosity of the rod and the rise time of the applied torque, these fluctuations become negligibly small and, as a result, only a 1-dimensional shear wave propagates in the rod.