Dynamic Problems for Piecewise Homogeneous Viscoelastic Bodies

Abstract

AbstractA non-stationary dynamic problem of linear viscoelasticity for a piecewise homogeneous body is considered for the case when the disturbed domain is finite. The interrelation between such a problem and the spectral problem of piecewise homogeneous body free oscillations is established. The structure of the eigenvalues set of the spectral problem is investigated. A method of searching for eigenvalues near the limit points of the spectral set is proposed. The integral Laplace transform in time is applied to the non-stationary dynamic problem for a linear viscoelastic piecewise homogeneous structure. For the case when each of the hereditary kernels is a finite sum of exponentials, the solution in the originals is presented as a series of residues at the points of the spectrum. Thus, the constructing of the non-stationary solution is reduced to the search for the elements of the spectral set. As an example, the solution to the plane axisymmetric problem of transient longitudinal waves’ propagation in a cross-section of a hollow infinitely long cylinder consisting of two coaxial elastic layers and a viscoelastic layer between them is constructed and discussed. As a result, it becomes possible to investigate and to reveal the influence of the piecewise inhomogeneity on the non-stationary waves’ propagation in a cylinder with viscoelastic and elastic layers.KeywordsDynamic problems of viscoelasticityPiecewise homogeneous bodiesWave processesLayered cylinder