Applicability of Four Parameter Viscoelastic Model for Longitudinal Wave Propagation in Non-Homogeneous Rods

This study is concerned to check the validity of a four parameter viscoelastic model for longitudinal wave propagating in the non-homogeneous viscoelastic rods of varying density. The rods are assumed to be initially unstressed and at rest. In this study, it is assumed that density ' ' , rigidity 'G' and viscosity ' ' of thespecimen i.e. rod are space dependent and obey the laws 2 1 0 e x , 2 2 0 G G e x and 2 3 0 e x . The method of non-linear partial differential equation (Eikonal equation) has been used for finding the dispersion equation of longitudinal waves in rods. A method for treating reflection at the free end of the finite nonhomogeneous viscoelastic rod is also presented. All the three cases taken in this study are discussed graphically.