Propagation of longitudinal waves in a linear viscoelastic medium

Abstract

The article is devoted to the study of longitudinal wave propagation in a viscoelastic medium. A mathematical model of the problem of a linear viscoelastic medium was developed. The solution to the considered problems is reduced to the solution of a system of differential equations solved by the method of characteristics with the appropriate boundary conditions. The results are compared with known results obtained by other authors; a comparison shows the adequacy of the task posed. It was determined that the maximum values of stress, strain, and velocity of particles in viscous media vary according to a non-linear law. In the initial section of the medium and near it, first, the stress reaches its maximum, and then the strain and velocity of particles reach their maximum values.