The Scattering Of Elastic Waves By Cavity In Exponentially Inhomogeneous Media

The problem of scattering caused by geometric discontinuities has always been the focus of the study on elastic dynamics.In recent years,the problems of propagation and intensity of wave in piezoelectric materials,the propagation path of wave using metamaterials,the analysis of wave problems in functionally graded materials and so on have drawn great attention from academia and engineering fields.In this paper,the separation variable method and conformal transformation method are used to solve the scattering problem of out-plane wave in an exponential inhomogeneous medium.Firstly,the mathematical model of inhomogeneous medium parameter is presented,which is the inhomogeneous medium with exponential density.There are two types of models.The wave number of the first model is a function related to the shape of the hole.The wave number of the second model is a function of positional coordinates.For the first inhomogeneous model,the wave equation for the scattering problem of SH-wave by elliptical holes in exponential media is a variable coefficient partial differential equation.The wave equation is converted to another complex plane by conformal transformation.By separating the variables,the variable coefficient partial differential equation is divided into two ordinary differential equations,and the infinite partialar solution is obtained by solving the two equations respectively.The solution of an integral form is obtained by stacking the special solution.By using Fourier series expansion,the general term of the series is observed,which is related to the integral expression of Hankel function.By discussing the integral path of the domain function,we analyze the different integral paths corresponding to different Bessel function types,and then we use the scattering wave as the series of Hankel function.Finally,the total wave field is obtained by superposition of the wave field,and the unknown coefficient is obtained by the boundary condition,thus the expression of the dynamic stress concentration factor is obtained.For the second inhomogeneous medium model,the scattering equation is also the variable coefficient equation.At this time,the equation is transformed into a standard form by conformal transformation,and finally the solution of the scattering wave equation is obtained.By analyzing the distribution of dynamic stress concentration factor,this paper expounds the influence of factors such as non-uniform parameters,reference wave number,pore shape and hole depth on the degree of stress concentration,and the reasons for the change of the dynamic stress concentration distribution with the influence factors are analyzed.