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Influence of Rigid, Stress-Free and Yielding Base of a Composite Structure on the Propagation of Rayleigh-Type Wave: A Comparative Approach

Published online by Cambridge University Press:  24 August 2017

A. Chattopadhyay ,
A. K. Verma ,
M. S. Chaki  and
A. K. Singh
A. Chattopadhyay
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, Jharkhand, India
A. K. Verma*
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, Jharkhand, India
M. S. Chaki
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, Jharkhand, India
A. K. Singh
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, Jharkhand, India
*
*Corresponding author (amitkverma.ismdhanbad@gmail.com.)
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Abstract

In this paper, case wise studies have been made to investigate the possibility of propagation of Rayleigh-type wave in a composite structure comprised of two transversely-isotropic material layers with viscoelastic effect. The common interface between the layers is considered to be rigid whereas the base has been considered as rigid, stress-free and yielding in three different cases (Case-I, II and III). Closed-form of frequency equation and damped velocity equation has been established analytically for propagation of Rayleigh-type wave in a composite structure for all three cases. In special cases, frequency equations and damped velocity equations for the case of composite structure with rigid, stress-free and yielding base have been found in well-agreement to the established standard results pre-existing in the literature. Numerical and graphical computation of phase and damped velocity of Rayleigh-type wave propagating in the composite structure comprised of double transversely-isotropic viscoelastic Taylor sandstone material layers (Model-I) and double isotropic viscoelastic material layers (Model-II) have been carried out. Significant effect of anisotropy and width ratio of layers, dilatational and volume viscoelasticity associated with viscoelasticity of layer medium and yielding parameter associated with yielding base of composite structure on phase and damped velocities of Rayleigh-type wave for the considered models have been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the present problem.

Keywords

Rayleigh-type wavesTransversely isotropic viscoelasticRigid baseYielding base
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 6 , December 2018 , pp. 733 - 748
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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