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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.

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.

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.

The paper is original and it is not published elsewhere.

The purpose of this study is to comprehend the efficiency levels of the Indian textile industry and also its sub-sectors in the light of changing global and national business environment. It is imperative to study the efficiency levels of textile industry for an emerging economy like India, where the industry contributes up to 13 per cent in export earnings, 10 per cent in total industrial production and 2 per cent in gross domestic product (GDP). The study holds an important place in the wake of phasing out of the quota regime existing under the Multi Fibre Agreement (MFA) and the rising competition being faced from countries such as Bangladesh, Vietnam and Cambodia.

The present study attempts to have an in-depth analysis of the efficiency levels in the Indian textile industry using meta-frontier data envelopment analysis, which is a non-parametric linear programming based frontier technique.

The findings highlight that the Indian textile industry is inefficient and has a huge scope of improvement in terms of efficiency. It also confirms the existence of different production functions among the sub-sectors of the industry. Among the different sub-sectors, the proximity of production frontier of readymade garments is the closest to meta-frontier followed by cotton and blended yarn, man-made fibre, cloth and others.

The findings bear strong implications for the policymakers in their attempt to regain the lost competitive position of the Indian textile industry and to enhance its contribution in the economy. As per the findings, policymakers should target the relatively inefficient sub-sectors of textile industry (cloth, man-made fibre, cotton and blended yarn) to infuse more efficiency in these sectors to enhance the market share of the Indian textile industry in the global textiles market.

The current study is a unique addition to the sparse literature on managing efficiencies in the textile industry, particularly of emerging economy like India. Looking at the methodological and geographical coverage of the previous work, it was found that no study has explored and analysed the efficiencies of the sub-sectors in the Indian textile industry using meta-frontier analysis. Therefore, this study will be the first of its kind which seeks to fill such gaps and intends to enrich the available literature.