Analysis of horizontally polarized shear waves on a highly inhomogeneous loaded bi-material plate

Maha M. Helmi; Ali M. Mubaraki; Rahmatullah Ibrahim Nuruddeen; Maha M. Helmi; Ali M. Mubaraki; Rahmatullah Ibrahim Nuruddeen

doi:10.3934/math.2023109

AIMS Mathematics

2023, Volume 8, Issue 1: 2117-2136. doi: 10.3934/math.2023109

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Analysis of horizontally polarized shear waves on a highly inhomogeneous loaded bi-material plate

1.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Federal University Dutse, P.O. Box 7156 Dutse, Jigawa State, Nigeria

Received: 07 September 2022 Revised: 15 October 2022 Accepted: 23 October 2022 Published: 28 October 2022
MSC : 26A33, 73D05

The current manuscript critically examines the propagation of horizontally polarized shear waves on the dispersion of a highly inhomogeneous thin bonded bi-material plate when a load due to the Winkler's elastic foundation is prescribed. An analytical procedure of solution is deployed for the study; in addition to the exploitation of effective boundary conditions approach for the asymptotic examination. The overall inference of the current study is the realization of the fact that the vibrational displacements in both layers are enhanced by an increase in the inhomogeneity parameter; at the same time lessened with an increment in the foundation parameter. Moreover, a perfect approximation of the dispersion relation has been realized, with its validity extending to almost the entire low-frequency range. Lastly, the influence of the material inhomogeneity has been noted to affect fundamental mode, as against the presence of the foundation parameter which affects the first harmonic curve. More so, an increase in the two parameters narrows the chances of low-frequency propagation.
- propagation of waves,
- bi-material plates,
- inhomogeneous media,
- analytical procedure,
- asymptotic approach
Citation: Maha M. Helmi, Ali M. Mubaraki, Rahmatullah Ibrahim Nuruddeen. Analysis of horizontally polarized shear waves on a highly inhomogeneous loaded bi-material plate[J]. AIMS Mathematics, 2023, 8(1): 2117-2136. doi: 10.3934/math.2023109

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Abstract

The current manuscript critically examines the propagation of horizontally polarized shear waves on the dispersion of a highly inhomogeneous thin bonded bi-material plate when a load due to the Winkler's elastic foundation is prescribed. An analytical procedure of solution is deployed for the study; in addition to the exploitation of effective boundary conditions approach for the asymptotic examination. The overall inference of the current study is the realization of the fact that the vibrational displacements in both layers are enhanced by an increase in the inhomogeneity parameter; at the same time lessened with an increment in the foundation parameter. Moreover, a perfect approximation of the dispersion relation has been realized, with its validity extending to almost the entire low-frequency range. Lastly, the influence of the material inhomogeneity has been noted to affect fundamental mode, as against the presence of the foundation parameter which affects the first harmonic curve. More so, an increase in the two parameters narrows the chances of low-frequency propagation.

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