DYNAMIC PROBLEM FOR A VISCOELASTIC HOLLOW CYLINDER WITH COAXIAL ELASTIC INCLUSION

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.

Automated summary

This study considers the non-stationary longitudinal wave propagation in the cross-section of an infinite hollow linear-viscoelastic cylinder with coaxial elastic inclusion. The continuity of displacements and stresses on the contact surfaces between the layers is assumed. The solution is constructed using the integral Laplace transform in time with subsequent reversal. For the case when each relaxation kernel is a finite sum of exponentials, the original problem is presented as a series of residues. Therefore, the process of constructing a non-stationary solution reduces to finding the roots of the characteristic transcendental equation. The derived solution allows for the investigation of transient wave propagation in a viscoelastic cylinder with specified initial data and coaxial elastic inclusion.