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

AIMS Mathematics

article

Maha M. Helmi¹  Ali M. Mubaraki¹  Rahmatullah Ibrahim Nuruddeen² 

[1] Department of Mathematics and Statistics, College of Science, Taif University;Department of Mathematics, Faculty of Science, Federal University Dutse

关键词: propagation of waves;    bi-material plates;    inhomogeneous media;    analytical procedure;    asymptotic approach;   

DOI  :  10.3934/math.2023109

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY