Dynamic Problem for a Viscoelastic Hollow Cylinder with Coaxial Elastic Inclusion

Abstract

A problem of non-stationary longitudinal wave propagation in the cross-section of an infinite hollow linear-viscoelastic cylinder with coaxial elastic inclusion is considered. On the contact surfaces between the layers, continuity of displacements and stresses is assumed. The solution of the problem is constructed using the integral Laplace transform in time with subsequent reversal. For the case when each of the relaxation kernels is a finite sum of exponentials, the original is presented as a series of residues. Thus, the process of constructing a non-stationary solution is reduced to the search for the roots of the characteristic transcendental equation. The derived solution allowed to investigate the transient wave propagation in a viscoelastic cylinder with coaxial elastic inclusion with specified initial data.