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Journal of Applied Mathematics
Volume 2017, Article ID 2095425, 6 pages
https://doi.org/10.1155/2017/2095425
Research Article

Nonlinear Waves in Rods and Beams of Power-Law Materials

1Department of Mathematics, School of Science and Technology, Nazarbayev University, Astana 010000, Kazakhstan
2Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China

Correspondence should be addressed to Dongming Wei; zk.ude.un@iew.gnimgnod

Received 16 March 2017; Revised 4 May 2017; Accepted 4 June 2017; Published 13 July 2017

Academic Editor: Xin-Lin Gao

Copyright © 2017 Dongming Wei 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

Some novel traveling waves and special solutions to the 1D nonlinear dynamic equations of rod and beam of power-law materials are found in closed forms. The traveling solutions represent waves of high elevation that propagates without change of forms in time. These waves resemble the usual kink waves except that they do not possess bounded elevations. The special solutions satisfying certain boundary and initial conditions are presented to demonstrate the nonlinear behavior of the materials. This note demonstrates the apparent distinctions between linear elastic and nonlinear plastic waves.