Rheological Response and Validity of Viscoelastic Model Through Propagation of Harmonic Wave in Non-Homogeneous Viscoelastic Rods

This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e. rod are space dependent. The method of non-linear partial differential equation (Eikonal equation) has been used for finding the dispersion equation of harmonic waves in the rods. A method for treating reflection at the free end of the finite non-homogeneous viscoelastic rod is also presented. All the cases taken in this study are discussed numerically and graphically with MATLAB.

Keywords:

Harmonic waves , Viscoelastic media , Friedlander series , Inhomogeneous , Varying density