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A multi-layered model of poroelastic, HSTI, and inhomogeneous media to study the Love-type wave propagation due to an impulsive point source: a Green’s function approach

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Abstract

The propagation of Love-type waves due to an impulsive point source in a hydrostatic stressed transversely isotropic (HSTI) strip clamped between a poroelastic strip and an inhomogeneous semi-infinite elastic half-space is studied. Both the strips are of finite thickness, and the semi-infinite half space is considered spatial-dependent inhomogeneous medium. The Dirac-delta function has been taken into account to represent the impulsive point source force, and Fourier Transform is used to simplify the governing equations for the respective media. Green’s functions technique has been adopted for solving the problem using boundary conditions of the considered problem. Thereafter, a closed-form dispersion equation has been obtained for the model. This dispersion equation infers lots of information about the considered wave into the structure. For numerical simulation purposes, we have taken six material examples of a transversely isotropic strip under the hydrostatic stress, namely Beryl, Magnesium, Cadmium, Zinc, Cobalt, and simply isotropic. The impacts of involved parameters on the phase velocity of the wave have been studied extensively and comparatively in 6 numerical examples of HSTI media. It is reported that the phase velocity of the Love-type wave is more pronounced in the presence of porosity, hydrostatic stress, linear and quadratic inhomogeneities as well as the thickness variations in both layers. Both the linear and quadratic enhance the phase velocity of the wave, while the porosity and hydrostatic stress helping to diminish the phase velocity.

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Acknowledgements

The authors Venkatesan P (Ph.D. Reg. No. 22PHD0124) and Dr. Parvez Alam thank Vellore Institute of Technology, Vellore for providing ‘VIT SEED Grant-RGEMS Fund (Sanction order No.:SG20220003)’ for carrying out this research work.

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  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India

    P. Venkatesan & Parvez Alam

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  1. P. Venkatesan
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  2. Parvez Alam
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Correspondence to Parvez Alam.

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Venkatesan, P., Alam, P. A multi-layered model of poroelastic, HSTI, and inhomogeneous media to study the Love-type wave propagation due to an impulsive point source: a Green’s function approach. Acta Mech 235, 409–428 (2024). https://doi.org/10.1007/s00707-023-03760-7

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