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Effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a heterogeneous half-space

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Abstract

In the present paper we study the effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a semi-infinite heterogeneous half-space, where the heterogeneity is both in rigidity and density. The present study demonstrates that torsional waves can propagate in the layer. The velocities of torsional waves have been calculated numerically as a functions of KH, (where K is the wave number and H is the thickness of the layer) and are presented in a number of graphs. It is also observed that, for a layer over a homogeneous half-space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary whereas it does at the free boundary.

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Abbreviations

H :

Thickness of the layer

μ :

Rigidity of the medium

ρ :

Density of the medium

a and b :

Constants having dimensions that are inverse of length

σ ij :

Stress components

u, v and w :

Displacement components in radial, circumferential and axial directions, respectively

Ω :

Dilatation

δ ij :

Kronecker delta

e ij :

Components of strains

K :

Wave number

ω :

Circular frequency

c :

Velocity of torsional wave

c 0 :

Velocity of shear wave in the layer

c 1 :

Velocity of shear wave in the half-space

A 1, A 2 and D :

Arbitrary constants

γ and R :

Dimensionless quantities

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian School of Mines University, Dhanbad, 826004, India

    S. Gupta, A. Chattopadhyay & S. Kundu

  2. Department of Physics, Asansol Engineering College, Asansol, 713304, India

    A. K. Gupta

Authors
  1. S. Gupta
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  2. A. Chattopadhyay
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  3. S. Kundu
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  4. A. K. Gupta
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Correspondence to S. Gupta.

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Gupta, S., Chattopadhyay, A., Kundu, S. et al. Effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a heterogeneous half-space. Arch Appl Mech 80, 143–150 (2010). https://doi.org/10.1007/s00419-009-0303-4

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  • DOI: https://doi.org/10.1007/s00419-009-0303-4

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