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Implementation of finite difference approximation on the SH-wave propagation in a multilayered magnetoelastic orthotropic composite medium

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Abstract

This paper presents an outcome of the broader effect to assess the importance of magnetoelasticity, compressive and tensile initial stress in soil dynamics. Haskell’s matrix technique is employed to investigate the SH-wave propagation in a multilayered magnetoelastic orthotropic (MMO) medium. The dispersion relation for the total (\(n-1\)) layers lying over a half-space is obtained in a closed form. Special cases are derived for both the single and double layers, and the obtained relations are found to be in good agreement with the Classical Love wave equation. Based on the finite difference technique, a stability analysis is performed to reduce the escalation of errors to make it stable and convergent. The expression for the phase and group velocities is attained by this technique when the SH-wave propagates across the MMO medium. Numerical computations and graphical exhibition have been carried out to show the effects of different values of the magnetoelastic coupling parameter, compressive and tensile initial stresses and courant number on the phase and group velocities.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, Jharkhand, 826004, India

    Shishir Gupta & Neelima Bhengra

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  1. Shishir Gupta
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  2. Neelima Bhengra
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Correspondence to Neelima Bhengra.

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Gupta, S., Bhengra, N. Implementation of finite difference approximation on the SH-wave propagation in a multilayered magnetoelastic orthotropic composite medium. Acta Mech 228, 3421–3444 (2017). https://doi.org/10.1007/s00707-017-1884-6

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  • DOI: https://doi.org/10.1007/s00707-017-1884-6

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