Non-homogeneous polymer model for wave propagation and its rheological response

Abstract

This article concerns certain aspects of four parameter polymer models to study harmonic waves in the non-homogeneous polymer rods of varying density. There are two sections of this paper, in first section, the rheological behaviour of the model is discussed numerically and then it is solved analytically with the help of Friedlander Series using Eikonal equation of optics. The model is chosen for studying viscous, elastic and retarded elastic response to shearing stress. In another section, the applicability of the developed model is studied through wave propagation in polymer non-homogeneous rods. We have used linear partial differential equations for finding the dispersion equation of waves in the polymers. The rheological behaviour of four-parameter viscoelastic models under dynamic loading is also discussed in detail. All the cases taken in this study are discussed analytically and numerically with MATLAB.

Keywords: Harmonic Waves; Friedlander Series; Inhomogeneous; Varying Density