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Applied Mathematics and Mechanics

, Volume 39, Issue 3, pp 317–334 | Cite as

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

  • P. Singh
  • A. Chattopadhyay
  • A. K. Singh
Article
  • 83 Downloads

Abstract

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano’s and Ferrari’s methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

Keywords

Rayleigh-type wave inhomogeneity initial stress visco-elasticity incompressible 

Chinese Library Classification

O353 

2010 Mathematics Subject Classification

74J15 

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Notes

Acknowledgements

Ms. P. SINGH conveys her sincere thanks to Indian Institute of Technology (Indian School of Mines), Dhanbad, India for providing Junior Research Fellowship.

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (ISM)DhanbadIndia

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