Scattering Of Anti-plane Waves By Convex Boundary With Embedded Circular Hole In Anisotropic Medium

Because stress wave plays an important role in manufacturing,military technology and scientific research,it has been an important direction of mechanical research in recent years,and anisotropic materials are an important branch of stress wave development,which are widely distributed in nature and artificial synthesis.For materials,some specific characteristics of wave can be achieved by setting special boundaries and arranging inclusions,which provide important application prospects for sensor design,vibration reduction and buffering,detection target recognition,and seismic analysis.Based on the typical convex interface and the internal cavity,this paper studies the propagation characteristics of anti-plane elastic waves in anisotropic media.The wave equation of anisotropic medium in complex domain is solved,and the mapping function from anisotropic medium to isotropic medium is calculated in detail;For the complex convex boundary,the region matching technology is used to divide it into expressible sub regions,and introduces a new method for solving algebraic equations.The singularity of reflex angle is proposed,and effective solutions are given.First,in the isotropic medium,based on the separation variable method,this paper deduces the complex fractional wave function which satisfies the free boundary condition of the wedge-shaped edge;the wave equation which satisfies the half-space free boundary condition is deduced by the symmetry method;the auxiliary circle is used to solve the singularity problem of reflex angle in the wedge;based on multipolar coordinate method and region matching technology,algebraic equations under auxiliary boundary conditions and free boundary conditions are established in complex domain;and discrete boundary least squares method is used to solve the algebraic equations for undetermined coefficient.Second,in the anisotropic medium,according to the wave equation of the plane wave from the anisotropic medium,the mapping function and the mapping coordinate system from the anisotropic medium to the isotropic medium are deduced,and the conformal property and stress constitutive of the mapping function are obtained.Based on isotropic medium theory,with the help of isotropic medium mapping space,the wave-displacement function satisfying the zero-stress boundary condition is deduced by the separation variable method and the symmetry method.In the frequency domain,the singularity auxiliary circle radius,auxiliary boundary discrete number and expansion series are determined through accuracy and convergence analysis;and through auxiliary boundary continuity,free boundary zero stress condition,degradation model comparison and secondary development of finite element method for the material constitutive relation,verify the validity of singularity auxiliary circle,fractional wave function,symmetry method,boundary discrete least square method and anisotropic mapping function.Finally,triangular or trapezoidal boundary with inner circular hole as typical structure,the free interface displacement and cavity stress are studied for different frequency of the incident wave,the incident angle,the shape of the convex interface,the position of the circular hole,and the material,in the frequency domain.On the basis of the frequency domain theory,the transfer function is established,and the propagation and scattering processes of the wave around the convex interface and the cavity in the time domain,are obtained through the inverse Fourier transform.