Surface Waves on a Coated Homogeneous Half-Space under the Effects of External Forces

The present study focuses on the examination of the propagation of plane surface waves on a coated half-space, which is accompanied by the magnetic field force, and the normal mechanical loading, due to Winkler’s elastic foundation. The study is based upon the application of the analytical and asymp...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-11, Vol.14 (11), p.2241
Main Authors: Mubaraki, Ali M., Almalki, Fadhel M.
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Boundary conditions
coated half-space
Crack propagation
Differential equations
Elastic foundations
Half spaces
magnetic field force
Magnetic fields
Mathematical analysis
Operators (mathematics)
Permeability
Propagation
Surface motion
Surface waves
Wave propagation
Wavelengths
Winkler’s elastic foundation
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Summary:The present study focuses on the examination of the propagation of plane surface waves on a coated half-space, which is accompanied by the magnetic field force, and the normal mechanical loading, due to Winkler’s elastic foundation. The study is based upon the application of the analytical and asymptotic integration procedures to acquire and further analyze the aspiring secular equation. Asymptotically, the influence of the coating layer is suppressed by deploying apposite effective boundary conditions that are ingrained on a long-wave approximation condition, to obtain the resulting pseudo-differential operator of the reduced equation of surface motion. In fact, the comparison between the two approaches yielded considerable agreement through the dependency plots, featuring the scaled velocity v/vR versus the dimensionless wavenumber K. Moreover, certain well-known results in the literature are obtained as liming circumstances of the present examination. Additionally, an insightful finding about the vanishing possibility of the coating layer is illustratively highlighted.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14112241