Scattering Of Elliptical Hole In A Semi Space And Elliptical Inclusion On SH Waves At Nanoscale

In the field of new materials,with the continuous progress of nano-science and technology,nanometer materials have become the most dynamic research object with great influence on future social development.Due to the large specific surface area,the surface effects of nanometer materials cannot be ignored.Researchers have paid great attention to the research and development of nanoma terials by using surface effect in recent years.Up to now,many studies on surface effect are basically limited to nanometer cylindrical and spherical cavities,inclusions and other problems with constant curvature,and relatively few scattering studies on variable curvature cavities and inclusions,especially for the scattering in the half space.In this paper,based on the classical elastic theory and the surface elasticity,the boundary conditions of the problems studied at the nanoscale are obtained by using the generalized Young-Laplace equation;the stress field and displacement field of SH-wave scattering by elliptic cavity and inclusion under complex plane are derived by using conformal mapping and complex function method.The main contents are as follows:(1)For the scattering problem of plane SH wave by elliptic cavity in the half space at nanoscale,the dynamic stress concentration factor which can reflect the stress distribution around the cavity is obtained.The effects of surface effect,incident frequency and elliptic cavity ratio on the dynamic stress concentration factor around the cavity are discussed as the specific examples.(2)For the scattering problem of plane SH wave by elliptic inclusion at nanoscale,the dynamic stress concentration factor which can reflect the stress distribution around the inclusion is obtained.The effects of surface,incident angle,incident frequency and material constants of elliptic inclusion on the dynamic stress concentration factor around the inclusion are discussed respectively.The results show that the surface effects have significant influence on the distributions of stresses around the elliptic cavity and inclusion.