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

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  • Ahmad Barzkar
  • Hojatollah Adibi

Abstract

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.

Suggested Citation

  • Ahmad Barzkar & Hojatollah Adibi, 2015. "On the Propagation of Longitudinal Stress Waves in Solids and Fluids by Unifying the Navier-Lame and Navier-Stokes Equations," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, April.
    • Handle: RePEc:hin:jnlmpe:789238
    DOI: 10.1155/2015/789238
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