Scattering Of SH Wave By Variable Curvature Density At Nanometer Scale

With the rapid progress and development of material science and the technology,a variety of new nano-materials for those unique properties are becoming mare of a concern.At present,one of the researches on nanomaterials at home and abroad is mainly focuses on surface effects and based on homogeneous continuous medium.With the increasing demands for new functional materials,the mechanical properties of inhomogeneous continuous environments have become a hot research topic,especially the influences of inhomogeneous medium on the scattering wave are remarkable.Nowadays,there are few studies on the wave scattering by inhomogeneity at the nanometers,even if there is limited at the macro scale.Based on the classical wave theory,complex function method and surface elasticity theory,the scattering of plane shear wave by nano-holes embedded in the density-varying medium is studied in this paper.According to the wave theory,the displacement potential functions of incident wave and reflect wave are determined respectively.And combining with the generalized Young-Laplace boundary conditions,the stress fields with unknown coefficients are constructed,then the coefficients are obtained by using the mathematical soft wave.In the various density-varying medium,the effects of the nano-cavity on the scattering of SH wave are got in the different conditions.The main tasks of this project are:(1)The scattering of plane SH waves by the circular nano-cavities embedded in the one-dimensional density-varying medium is studied.The wave field of incident and scattered waves is solved by Helmholtz equation to obtain the dynamic stress concentration factor around the nano-cavity.(2)The scattering of plane SH waves by the cylindrical cavities in inhomogeneous media with two-dimensional varying density is studied.The wave fields of incident and scattered waves in the two-dimensional density-varying medium are obtained.The effects of various factors on the dynamic stress concentration factor are analyzed by numerical simulation.The purpose of this paper is to simulate the non-uniform material model which is more close to the practical problem,namely the variable density new material.In the numerical simulation,the effects of variable density,surface effect and wave number on the stress around the circular cavities are discussed.The results show that they have significant effects on the stress around the cavities.