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Mathematical Problems in Engineering
Volume 2015, Article ID 789238, 9 pages
Research Article

On the Propagation of Longitudinal Stress Waves in Solids and Fluids by Unifying the Navier-Lame and Navier-Stokes Equations

Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, 424 Hafez Avenue, P.O. Box 15875-4413, Tehran, Iran

Received 2 September 2014; Accepted 14 December 2014

Academic Editor: Florin Pop

Copyright © 2015 Ahmad Barzkar and Hojatollah Adibi. 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.


Propagation of mechanical waves’ phenomenon is the result of infinitely small displacements of integrated individual particles in the materials. These displacements are governed by Navier-Lame and Navier-Stokes equations in solids and fluids, respectively. In the present work, a generalized Kelvin-Voigt model of viscoelasticity has been proposed with the aim of bridging the gap between solids and fluids leading to a new concept of viscoelasticity which unifies the Navier-Lame and the Navier-Stokes equations. On solving this equation in one dimension, propagation of stress disturbance in the so-called “Kelvin-Voigt materials” will be studied. The model of these materials involves all the elastic and viscoelastic solids, as well as fluids and soft materials.