Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (10): 1239-1252.doi: https://doi.org/10.1007/s10483-012-1618-7

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Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer

S. GUPTA, S. K. VISHWAKARMA, D. K. MAJHI, S. KUNDU   

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, Jharkhand, India
  • 收稿日期:2012-02-21 修回日期:2012-04-09 出版日期:2012-10-10 发布日期:2012-10-10
  • 通讯作者: S. GUPTA, Professor, Ph.D., E-mail: shishir_ism@yahoo.com E-mail:shishir_ism@yahoo.com

Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer

S. GUPTA, S. K. VISHWAKARMA, D. K. MAJHI, S. KUNDU   

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, Jharkhand, India
  • Received:2012-02-21 Revised:2012-04-09 Online:2012-10-10 Published:2012-10-10

摘要: The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types namely exponential, quadratic, and hyperbolic discussed separately. Dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equation of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.

关键词: torsional wave, phase velocity, crustal layer, exponential, quadratic, hyperbolic, copmpoate compresson.backing GKRR maim comem

Abstract: The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types namely exponential, quadratic, and hyperbolic discussed separately. Dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equation of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.

Key words: torsional wave, phase velocity, crustal layer, exponential, quadratic, hyperbolic, copmpoate compresson.backing GKRR maim comem

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