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Journal of Engineering Mathematics

, Volume 90, Issue 1, pp 1–11 | Cite as

Propagation of torsional waves in an inhomogeneous layer sandwiched between inhomogeneous semi-infinite strata

  • Pato Kumari
  • V. K. Sharma
  • Chitra Modi
Article

Abstract

The present work deals with the propagation of torsional waves in an inhomogeneous layer sandwiched between inhomogeneous semi-infinite strata. The superstratum has exponential variation in rigidity and density, whereas inhomogeneities in the layer and the substratum are assumed to arise due to linear and quadratic variations in shear modulus and density. Closed-form solutions for displacements in the layer and the semi-infinite strata are obtained. A generalized implicit dispersion equation is obtained for the phase velocity and expressed in terms of Heun functions and their derivatives. Three possible torsional modes are derived and characterized separately. It is observed that the effects of inhomogeneity parameters are different for different modes of torsional waves and certain torsional modes are found to be independent of certain inhomogeneity parameters. The range of confinement of torsional modes, the combined effect of wave number and inhomogeneity ratio, and the condition of torsional waves becoming nondispersive are derived through numerical simulation and shown using two-dimensional and three-dimensional graphs.

Keywords

Bessel function Heun confluent function Heun function Inhomogeneous semi-infinite media Phase velocity Quadratic inhomogeneity variation Torsional surface waves 

Notes

Acknowledgments

The authors are grateful to the reviewers for their constructive suggestions on the paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsJaypee Institute of Information TechnologyNoida India
  2. 2.Institute for Systems Studies & Analyses, DRDODelhi India

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