Effects of Surface Energy on Scattering of SH Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

Abstract:

When the radius of materials and structral devices reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of anti-plan shear waves by an elastic half-plan with a semi-cylindrical cavity considered the surface energy are investigated in this paper. When the boundary condition at the straight edge of the half-plan is traction free, the analytical solutions of stress fields of the half plan with semi-culindrical cavity are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of anti-plan shear waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. The effects of incident waves with different frequencies and incident angel, radius of semi-cylindrical cavity and surface energy on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

• Periodical: Advanced Materials Research (Volume 627)
• Pages: 698-704
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.627.698
• Online since: December 2012
• Authors: Zhi Ying Ou, Xiao Wei Liu, Qiong Deng
• Keywords: Dynamic Stress Concentration, Scattering, Sh Wave, Surface Energy

References

[1] Y. H. Pao, and C. C. Mow, Diffractions of Elastic Waves and Dynamic Stress Concentrations, Crane, Russak, New York (1973).

[2] M. D. Trifunac, Scattering of plane SH waves by a cylindrical canyon. Earthq. Eng. and Struct. Dyn., 1, 267-81(1973).

DOI: 10.1002/eqe.4290010307

[3] Z. P. Liao, J. P. Liu, Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section, Soli Dyn. and Earthq. Eng., 13, 407-412(1994).

DOI: 10.1016/0267-7261(94)90011-6

[4] Z. P. Liao, J. P. Liu, Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section, Earthq. Eng. and Struct. Dyn., 24, 1303-1313(1995).

DOI: 10.1002/eqe.4290241002

[5] M. E. Gurtin, A. I. Murdoch, A continuum theory of elastic material surfaces. Arch. Rat. Mech. Anal. 57, 291-323 (1975).

DOI: 10.1007/bf00261375

[6] Z. Y. Ou, G. F. Wang, T. J. Wang, Effect of residual surface tension on the stress concentration around a nanosized spheroidal cavity. Int. J. Eng. Sci. 46, 475-485(2008).

DOI: 10.1016/j.ijengsci.2007.12.008

[7] G. F. Wang, T. J. Wang, X. Q. Feng, Surface Effects on the Diffraction of Plane Compressional Waves by a Nanosized Circular Hole. J. Appl. Phys. 89, 231923 (2006).

DOI: 10.1063/1.2403899

[8] X. Q. Fang, L. L. Zhang, Dynamic stress around a cylindrical nano-inhomogeneity with an interface in a half-plane under anti-plane shear waves. Appl Phys A 106:625–633(2012).

DOI: 10.1007/s00339-011-6633-4