Energetic effects analysis of shear waves and their second harmonics in a waveguide with non-ideal component contact

Abstract

In this article the energetic and kinematic effects that occur in the elastic shear wave and its second harmonics propagation are investigated. The waveguide consists of anisotropic elastic crystal layer of cubic system m3m class enclosed between crystal halfspaces of same anisotropy class. A slipping contact is assumed in the contact zone of waveguide parts. The research is based on a model of general geometrical end physical nonlinearity in dynamic deformation processes. It allows to use elastic potential with the quadratic and cubic deformation components and the deformations with nonlinear terms. The approach of nonlinear elastic wave characteristics expansion into rows of a small parameter is used. Due to this approach at the first stage it's necessary to solve the problem of finding the components of the localized shear wave displacement vector (the problem of the first approximation). In the second stage, using the obtained results of the first approximation problem, the representation of the components of the displacement vector for the second harmonics of the localized elastic wave is solved in analytical form (the problem of the second approximation). By using the obtained kinematic results, the energy effects can be evaluated in the form of a vector of the average for the period of power flow. Specific results of the study of the amplitude-frequency and energy characteristics of the localized shear type elastic waves in the considered waveguide structure were obtained using computer algebra methods.The calculations of cinematic and energetic characteristics (that in contrast to linear SH harmonic are P-SV type waves) have been carried out for NaCl layer and germanium halfspaces waveguide.