On the propagation of longitudinal stress waves in solids and fluids by unifying the Navier-Lame and Navier-Stokes equations

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.