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Applied Mathematics and Mechanics

, Volume 34, Issue 2, pp 249–258 | Cite as

Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space

  • S. GuptaEmail author
  • D. K. Majhi
  • S. Kundu
  • S. K. Vishwakarma
Article

Abstract

The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson’s half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity.

Key words

Love waves initial stress heterogeneous half-space Gibson’s half-space dispersion equation phase velocity 

Chinese Library Classification

O347 

2010 Mathematics Subject Classification

74J15 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • S. Gupta
    • 1
    Email author
  • D. K. Majhi
    • 1
  • S. Kundu
    • 1
  • S. K. Vishwakarma
    • 1
  1. 1.Department of Applied MathematicsIndian School of MinesDhanbadIndia

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