On The Diffraction Of P/SV Wave By An Arbitrary Shaped Cavity At Nanoscale

Nanoscience and technology is a typical emerging comprehensive science and technology.In recent years,researching on nanomaterials has become a hot topic.Due to the increased the ration of surface area and volume of nanomaterials,the surface effects cannot be ignored.Using surface effects to develop nanoscale materials has been highly concerned by researchers,so it is great significance to develop surface elasticity theory based on classical elastic mechanics.However,many studies on surface effects are basically limited to the scattering of elastic waves to obstacles such as nanoscale cylindrical and spherical pores and inclusions with constant curvature,there are relatively few studies on the problem of variable curvature cavity.Based on the theory of surface elasticity,the scattering field and stress concentration of P/SV waves in a nanoscale arbitrary hole are studied.Since the hole is arbitrary shape,the wave function field cannot be directly constructed,which makes the problem more complicated.Therefore,the conformal transformation method is used to convert it into a unit circular hole,and the problem is transformed into scattering problem of planar P/SV waves of a circular hole at the nanoscale.The scattering field under the complex plane is given by the conformal mapping,the wave function expansion method and the complex function method.Getting a set of infinite algebraic equations that determine the unknown coefficients.By intercepting finite terms,using computer to solve.Taking the elliptical cavity as an example,the influence of surface parameter,the ratio of the major and minor axis of the ellipse and dimensionless wave number on dynamic stress concentration factor are discussed.The results show:(1)At low frequency incidence,the smaller the surface parameter is,the larger the dynamic stress concentration factor(DSCF)at the elliptical boundary is.For the high frequency incident wave,the stress concentration phenomenon becomes complicated,and the DSCF image at the elliptical boundary appears with a plurality of asymmetric peaks;(2)At low frequency incidence,the image is symmetric about?(28)?/2,and the smaller the ratio of the elliptical major axis and the minor axis is,the larger the DSC F around the elliptical cavity boundary is;(3)For incident P waves,when the surface parameter is relatively large,the smaller the dimensionless wave numberk_p a is,the larger the DSCF near the elliptical boundary is.For the incident SV wave,when the surface parameter is relatively large,with the dimensionless wave number k_s a increasing,the DSCF image changes more intensely and presents multiple peaks.