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Applied Mathematics and Mechanics

, Volume 36, Issue 8, pp 1045–1056 | Cite as

Propagation, reflection, and transmission of SH-waves in slightly compressible, finitely deformed elastic media

  • M. ChatterjeeEmail author
  • A. Chattopadhyay
Article

Abstract

The propagation, reflection, and transmission of SH waves in slightly compressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressible, finitely deformed layer overlying a slightly compressible, finitely deformed half-space is derived. The present paper also deals with the reflection and refraction (transmission) phenomena due to the SH wave incident at the plane interface between two distinct slightly compressible, finitely deformed elastic media. The closed form expressions for the amplitude ratios of reflection and refraction coefficients of the reflected and refracted SH waves are obtained from suitable boundary conditions. For the numerical discussions, we consider the Neo-Hookean form of a strain energy function. The phase speed curves, the variations of reflection, and transmission coefficients with the angle of incidence, and the plots of the slowness sections are presented by means of graphs.

Keywords

slightly compressible SH wave propagation inhomogeneity reflection transmission slowness section 

Chinese Library Classification

O343 

2010 Mathematics Subject Classification

74J15 74E05 74E10 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian School of MinesDhanbad JharkhandIndia

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