Propagation of Non-Stationary Waves in Viscoelastic Strip Composed of Orthotropic Layers

Abstract

Abstract. The analytical solution for transient waves caused by transverse impact on an infinite layered strip with free-free boundaries is presented in this work. The strip is composed of two horizontal layers of different heights. The materials of both layers are assumed to be linear viscoelastic and orthotropic. The case of special orthotropy is assumed for simplicity. The dissipative behaviour of each layer is modelled by the discrete model of standard linear viscoelastic solid in Zener configuration. The solving procedure used in this work follows the methods applied in previously published works dealing with the problems of a viscoelastic orthotropic strip and the symmetric case of a layered strip. The system of four linear partial integro-differential equations describing the non-stationary state of plane stress in the strip is solved by means of integral transform method. Concretely, the Laplace transform in time domain and the Fourier transform in spatial domain are applied. As a results of this procedure, the final formulas for displacement components in both layers are derived in Laplace domain. These transforms contain eight spectra of Fourier integrals which can be found as the solution of the system of eight complex equations arising from boundary conditions of the problem. When the spectra are known, the resulting formulas for the Laplace transforms of displacement components are obtained.The presented new formulation of non-symmetric problem enables to study the wave phenomena in general two-layered solids of strip-like geometry and it is fundamental for solving a problem with arbitrary number of layers.