ON THE PROBLEM OF NON-STATIONARY WAVES PROPAGATION IN A LINEAR-VISCOELASTIC LAYER

In this work a solution is presented of one-dimensional problem for non-stationary waves propagation in an infinite linear viscoelastic layer. The hereditary properties of the layer are described by the Boltzmann-Volterra model with a specific class of hereditary kernels. The Laplace transform technique is applied to solve the initial-boundary value problem with subsequent inversion. Depending on the type of hereditary kernels, the solution of the problem in terms of originals is presented in different forms. The solution is valid for the entire time range without the restriction for smallness of viscosity. The obtained solution allows to investigate the transient wave propagation process in a layer for given constitutive functions and parameters. It is demonstrated how hereditary kernels of different types, satisfying appropriate conditions, can have the same effect on the wave propagation.

Automated summary

This work presents a solution to the problem of one-dimensional non-stationary wave propagation in an infinite linear viscoelastic layer, using the Boltzmann-Volterra model to describe hereditary properties. The Laplace transform technique is applied and depending on the hereditary kernels, different forms of the solution are presented. The obtained solution allows for investigation of transient wave propagation process in the layer without restriction for viscosity. It is shown how different types of hereditary kernels can have the same effect on wave propagation under appropriate conditions.