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Advances in Mathematical Physics
Volume 2017, Article ID 5236898, 8 pages
https://doi.org/10.1155/2017/5236898
Research Article

The Analytical Form of the Dispersion Equation of Elastic Waves in Periodically Inhomogeneous Medium of Different Classes of Crystals

1S. Toraighyrov Pavlodar State University, Pavlodar 140008, Kazakhstan
2Sukkur Institute of Business Administration, Sindh, Pakistan
3University of California, Davis, CA 95616, USA

Correspondence should be addressed to Abdul Qadir; kp.ude.kus-abi@ridaqa

Received 28 March 2016; Revised 28 June 2016; Accepted 16 November 2016; Published 29 January 2017

Academic Editor: André Nicolet

Copyright © 2017 Nurlybek A. Ispulov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The investigation of thermoelastic wave propagation in elastic media is bound to have much influence in the fields of material science, geophysics, seismology, and so on. The heat conduction equations and bound equations of motions differ by the difficulty level and presence of many physical and mechanical parameters in them. Therefore thermoelasticity is being extensively studied and developed. In this paper by using analytical matrizant method set of equation of motions in elastic media are reduced to equivalent set of first-order differential equations. Moreover, for given set of equations, the structure of fundamental solutions for the general case has been derived and also dispersion relations are obtained.