Rheological behaviour and applicability of viscoelastic model for wave propagation in non-homogeneous polymer rods

Abstract

Purpose

This purpose of this paper is to discuss certain aspects of five-parameter viscoelastic 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. In another section, the applicability of the developed model is studied through harmonic wave propagation in polymer non-homogeneous rods. The authors have used linear partial differential equations for finding the dispersion equation of harmonic waves in the polymers. All the cases taken in this study are discussed analytically and numerically with MATLAB.

Design/methodology/approach

A five-parameter viscoelastic model constituting of three dash-pots D ₂(η ₂), D _2′(η _2′), D ₃(η ₃) and two springs S ₁(G ₁), S ₂(G ₂) is considered. Where, G ₁, G ₂ are the modulli of elasticity and η ₂, η _2′, η ₃ are the Newtonian viscosity coefficients of the considered model, respectively. The parameters of the model are non-homogeneous in nature, i.e. module of elasticity and viscosity coefficients are space dependent. 1D problem is formed by taking the material in the form of rod of inhomogeneous polymer material by taking one end at x=0. The co-ordinate x is measured positive in the direction of the axis of the filament.

Findings

When the density, rigidity and viscosity all are equal for the first material specimen, the sound speed is constant, i.e. non-homogeneous has no effect on speed and phase of the wave is given. So it becomes the case of semi non-homogeneous medium (a medium when characteristics are space dependent while the speed is independent of space variable). The use of five-parameter models is mostly restricted in the field of rock mechanics. Thus, these models can be used in determining the time-dependent behaviour of a polymer medium.

Originality/value

The paper is original and it is not published elsewhere.

Citation

Kakar, R., Kakar, S. and Kaur, K. (2014), "Rheological behaviour and applicability of viscoelastic model for wave propagation in non-homogeneous polymer rods", Multidiscipline Modeling in Materials and Structures, Vol. 10 No. 1, pp. 36-58. https://doi.org/10.1108/MMMS-03-2013-0025