Surface Effects on the Diffraction of P Wave by an Arbitrary Shaped Cavity

Zhiying Ou,Hongjun Han

doi:10.4236/ojapps.2019.96036

Abstract

This paper presents the effects of surface effects in the cavity of variable curvature. The wave function expansion method and the conformal mapping method are used in the solution of dynamic stress concentration factor around an irregularly shaped cavity at nano-scale. The stress boundary conditions on the surface are obtained by using the generalized Young-Laplace equation. The results show that the degree of stress concentration becomes more obvious with curvature increasing. Taking the elliptical cavity as an example, the influence of the ration of the major and minor axis of the ellipse, the numbers of the incident wave and the surface effects on the dynamic stress concentration factor are analyzed. The ration of the major and minor axis, the incident wave frequency and the surface effects show the pronounced effects on the dynamic stress concentration distributions.

Highlights

Nano-structured materials and nano-sized structural elements have unique mechanical and physical properties
This paper presents the effects of surface effects in the cavity of variable curvature
The wave function expansion method and the conformal mapping method are used in the solution of dynamic stress concentration factor around an irregularly shaped cavity at nano-scale

Summary

Introduction

Nano-structured materials and nano-sized structural elements have unique mechanical and physical properties. Using of surface elasticity theory, Lei et al [6] studied the effects of surface stress on the contact problem at nanometers, in which the contact mechanical properties are remarkably different from those in bulk solids. In the framework of surface elasticity theory, the scattering of plane compressional and shear waves by a single nano-sized coated fiber and the multiple scattering by two cylinder inclusions, which embedded in an elastic matrix is studied by Ou and Lee using the method of eigenfunction expansion [7] [8]. The results show that surface energy has a significant effect on the scattering of plane P wave as the radius of the semi-cylindrical inclusions shrink to nanometers. J. Han mainly studies the diffraction of P wave by arbitrary shape cavity at the nano-scale, and gives a method for estimating the magnitude of the dynamic stress concentration factor (DSCF)

Wave Function

Solution of the Problem

Numerical Results and Discussion

Conclusion