On the thermodynamically consistent fractional wave equation for viscoelastic solids

Abstract

Since the well-known methods for the computation of harmonically induced LAMB waves in elastic plates cannot be applied directly to viscoelastic material, an enhanced material model is developed. It is based on fractional time derivatives and incorporates a fractional KELVIN-VOIGT model. A proof of the thermodynamic consistency of this model is given. On the basis of the developed material model, the fractional wave equation is derived which allows for the calculation of LAMB waves in viscoelastic solids. © 2011 Springer-Verlag.