Dynamic Stress Concentration Around The Inclusion In Different Inhomogeneous Media Under SH Wave

Since inhomogeneous medium exists widely in nature and engineering application,wave propagation in inhomogeneous medium has become a popular topic in scientific research and engineering application.However,inclusions are unavoidable in inhomogeneous medium,no matter it exists in nature or it is predetermined.Moreover,the dynamic stress concentration caused by different kinds of inclusions in inhomogeneous medium under elastic wave usually leads a high risk of damage and failure of the material.Because of the complexity of the governing equation of wave motion in inhomogeneous medium,analytical methods in solving wave propagation in inhomogeneous medium are still in progress.Considering different mechanical properties of inhomogeneous medium and the analytical solutions of wave motion in it,dynamic stress concentration around different inclusions in different kinds of inhomogeneous media is investigated in this article by complex function method.Firstly,governing equations of SH wave propagation in density inhomogeneous medium and inhomogeneous medium with density and shear modulus expressed by functions are constucted systematically.In the complex plane,methodologies of solving wave propagation problems are obtained aiming at different kinds of media.Considering the constitutive relation between displacement and stress,stresses in the media are derived using the chain rule.Secondly,SH wave scattering in the inhomogeneous medium with density varying two dimensionally is investigated.The density of the inhomogeneous medium is expressed as??x,y?=?₀[4?²?x²+y²?+4??x+?²].Aiming at the specific wave equation,a pair of polynomial function is applied to normalize the governing equation.With the help of the normalized governing equation,wave fields and stresses are obtained,and undertermined coefficients are solved by boundary conditions.Dynamic stress concentration factor around different inclusions?vacuum and solid?with various parameters is calculated and discussed.Subsequently,scattering of SH wave in the density vertically inhomogeneous half space is researched.The density of the density of vertically inhomogeneous half space is??y?=?₀?²exp?2?y?.Exponential transformation function is utilized to normalize the wave equation with variable coefficients.Using multi-polar coordinates system and image principle,incident wave,reflected wave and scattering wave in the half space are expressed analytically.Applying boundary conditions,undertermined coefficients are obtained.Then,distribution of dynamic stress concentration factor around different inclusions?vacuum and solid?are calculated and discussed.Finally,based on complex function method,SH wave scattering in varied-velocity exponentially inhomogeneous medium is studied.The density and the shear modulus of the medium are both exponentially inhomogeneous,which have the expressions of??x?=?₀[?²exp?2?x?+exp?2?x?]and??x?=?₀exp?2?x?.Applying the method of auxiliary function,the governing equation is transformed.The auxiliary function is combined by an exponential function and an auxiliary displacement?,the governing equation of displacement?is normalized with the help of a pair of exponential transformation function.Hence,the real displacements and stresses in the inhomogeneous medium is obtained.Applying boundary conditions of different inclusions?vacuum and solid?,dynamic stress concentration factor with various parameters is calculated and discussed.