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Influence of Loosely-Bonded Sandwiched Initially Stressed Visco-Elastic Layer on Torsional Wave Propagation

Published online by Cambridge University Press:  28 October 2016

A. K. Singh ,
Z. Parween ,
A. Das  and
A. Chattopadhyay
A. K. Singh
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
Z. Parween*
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
A. Das
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
A. Chattopadhyay
Affiliation:
Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)Dhanbad, India
*
*Corresponding author ([email protected])
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Abstract

Assumption that the common interfaces of the media are perfectly bonded may not be always true. Situation may arise that composition of the two medium may be responsible for weakening the contact between them. So, it becomes obligatory to consider a loosely bonded interface in such cases which may affect the propagation of elastic waves through them. This paper thrashes out the propagation of torsional surface wave in an initially stressed visco-elastic layer sandwiched between upper and lower initially stressed dry-sandy Gibson half-spaces, theoretically. Both the upper and lower dry-sandy Gibson half-spaces are considered to be loosely-bonded with the sandwiched layer. Mathematical model is proposed and solution in terms of Whittaker's and Bessel's function is obtained. Velocity equation is obtained in closed form, its real part deals with the dispersion phenomenon whereas its imaginary part provides the damping characteristics. Influence of heterogeneities, sandiness, gravity parameters, initial-stresses, loose-bonding and internal-friction on the phase and damped velocities of torsional wave are computed numerically and depicted graphically. Deduced dispersion equation and damped velocity equation matches with classical Love-wave equation and vanishes identically for the isotropic case respectively.

Keywords

Loosely-bondedVisco-elasticDry-sandy Gibson half-spaceTorsional wave
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 3 , June 2017 , pp. 351 - 368
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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