Scattering Of P Waves In Half Space On Nanometer Cylindrical Core-shell Structures

With the progress of science and technology,nanomaterials have received more and more attention and research.When the size of the material decreases,the ratio of surface area to volume of the material increases rapidly,making the physical and chemical properties of the material significantly different from the macroscopic conditions.Based on the theory of surface elasticity,the scattering of P wave by nanometer cylindrical core-shell structure in half space is studied.By using coordinate transformation method,wave function expansion method and orthogonality of trigonometric function,the dynamic stress concentration coefficients of core-shell structures at ideal and non-ideal interfaces are obtained respectively,and the calculated results are analyzed and discussed.The main research methods of this paper are as follows:(1)Fourier-Bessel series expansion method and orthogonality of trigonometric functions in complex domain are used to study the scattering of plane p-waves by cylindrical core-shell structures in half space.(2)The scattering of plane longitudinal waves by cylindrical core-shell structures with ideal and non-ideal interfaces in half space is discussed in detail.The results show that when the radius of the core-shell is close to nanometer,the surface energy has a significant effect on the diffraction of the elastic wave;under the action of different incident wave frequencies,the dynamic stress concentration coefficient will change significantly;when the buried depth of core-shell structure is large,the dynamic stress concentration coefficient will be stable within a range;with the increase of spring coefficient,the performance of the imperfect interface is close to the perfect interface.Using different spring models to simulate the imperfect interface for different practical problems can make the research results more accurate.