Scattering Of SH Waves By Circular Hole In Half Space And Right-angle Space Giant Magnetostrictive Medium

As one of the most potential functional materials in the 21 st century,the giant magnetostrictive material,namely,piezomagnetic material,plays an important role in military,marine,aerospace,navigation,medicine,mechanical engineering and other fields due to its extremely high magnetostrictive property.Due to the influence of force-magnetic coupling,processing technology,environmental change and brittleness of the material itself,such defects as circular hole may occur in the material.When the giant magnetostrictive shock absorber in civil engineering enters the working state,the mechanical vibration will occur inside the material,and the scattering will occur when the mechanical wave propagates in the process of the material if encountered the internal defects or interfaces,which will cause the displacement mutation,the stress concentration or the magnetic field intensity concentration at the defects or interfaces,then the strength of giant magnetostrictive material will be influenced.Therefore,we need to carry out dynamic analysis on the defects of giant magnetostrictive material and pay more attention to the scattering problem of elastic wave.For the above problems,in the present work,the study respectively discussed the impact of interface when the elastic wave propagation in magnetostrictive material or the impact of defects in the whole space medium,but when the material internal defects and external interfaces exist and interact with each other at the same time,the dynamic stress problem of giant magnetostrictive material has not been discussed for further.In this paper,the giant magnetostrictive medium model is simplified into half space and right-angle space models,then the dynamic behavior around the defect when the boundary and the defect coexist is considered,that is,the dynamic stress of the half space and right-angle space giant magnetostrictive medium with circular hole are studied.The purpose of this paper is to provide an effective theoretical analysis method for nondestructive testing and failure analysis of giant magnetostrictive materials in engineering practice.The specific research contents of this paper are as follows:The scattering problem of circular hole in half space giant magnetostrictive medium under steady SH wave is studied and the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular hole are given.Firstly,based on the linear constitutive equation of giant magnetostrictive medium,the anti-plane magnetoelastic coupling control equation is established.Then,based on the theory of complex function and the method of wave function expansion,the expression of the wave function of the incident wave,the reflected wave,the scattering wave,the magnetic potential corresponding to the incident wave,the magnetic potential corresponding to the reflected wave and the magnetic potential corresponding to the scattering wave that corresponding to the horizontal boundary stress free and magnetic insulation conditions are constructed by using the mirror method.Then,according to the boundary conditions of the circular hole boundary,an infinite linear equation set is established to solve the undetermined coefficients in the wave function expression.The infinite linear equation set is solved by combining the Fourier expansion method,and the equation set was truncated to meet the precision requirements to obtain the unknown coefficients.Finally,the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around the circular hole are obtained.The scattering problem of circular hole in giant magnetostrictive medium in right-angle space under the action of steady SH waves is studied.Based on the solution of the half space model,the vertical boundary of the right angle boundary is mirrored so that the wave function satisfies the stress freedom and magnetic insulation conditions of the vertical boundary.At this point,the right angle space problem will be transformed into the half-space problem.The effects of incident angle,incident wave frequency,distance between circular hole and horizontal boundary and vertical boundary,piezomagnetic coefficient and permeability on dynamic stress concentration factor and magnetic field intensity concentration factor around circular hole are given by numerical examples,and some valuable conclusions are also given.These conclusions are of certain reference value to the study of the material properties and nondestructive testing of the giant magnetostrictive material with circular hole defects.