Plane Wave Reflection in a Compressible Half Space with Initial Stress-Reference-Cited by-同舟云学术

Plane Wave Reflection in a Compressible Half Space with Initial Stress

Published:2019-01-01 Issue:1 Volume:17 Page:438-448
ISSN:2391-5471
Container-title:Open Physics
language:en
Short-container-title:

Author:

Shams Moniba¹,Khalique Chaudry Masood²,Aziz Taha²³

Affiliation:

1. Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology , Sector H-12 , Islamabad , Pakistan

2. International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences, North-West University , Mafikeng Campus , Private Bag X 2046, Mmabatho 2735 , South Africa

3. Department of Mathematics, Dammam Community College, King Fahd University of Petroleum and Minerals , KFUPM Box 5084 , Dhahran 31261 , Saudi Arabia

Abstract

Abstract In this paper, the problem of wave propagation in a compressible half-space with an initial stress is considered. General discussion on the speed of wave in the presence of an initial stress is presented. Furthermore, reflection of a homogeneous plane P−wave is also studied. A special strain energy function dependent on this initial stress is used to understand the response of the materials. Explicit formulas for the reflection coefficients are also presented. General nonlinear theory and the theory of invariants are used to derive theoretical results. Graphical illustration of theoretical results for various numerical values of parameters show that initial stress has considerable bearing on the behavior of a plane wave.

Publisher

Walter de Gruyter GmbH

Subject

General Physics and Astronomy

Link

https://www.degruyter.com/document/doi/10.1515/phys-2019-0044/pdf

Reference24 articles.

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3. Hoger A., On the residual stress possible in an elastic body with material symmetry, Arch. Ration. Mech. Anal., 1985, 88, 271-290.

4. Ogden R. W., Sotiropolous D. A., Reflection of plane waves from the boundary of a pre-stressed compressible half-space, IMA J. Appl. Math., 1998, 59, 95-121.

5. Biot M. A., Non-linear theory of elasticity and the linearized case for a body under initial stress, Philos. Mag., 1939, XXVII, 468-489.

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