 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12977 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8096
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| In English (Mech. Solids): | | 4881 |
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| << Previous article | Volume 59, Issue 5 / 2024 | Next article >> |
| Ali M. Mubaraki, Maha M. Helmi, Rahmatullah Ibrahim Nuruddeen, and Mounirah Areshi, "Propagation of Rayleigh-Type Waves on an Elastic Half-Space Covered by a Thin Multi-Layered Coating," Mech. Solids. 59 (5), 2906-2920 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
5 |
Pages |
2906-2920 |
| DOI |
10.1134/S0025654424604671 |
| Title |
Propagation of Rayleigh-Type Waves on an Elastic Half-Space Covered by a Thin Multi-Layered Coating |
| Author(s) |
Ali M. Mubaraki (Department of Mathematics and Statistics, College of Science, Taif University, Taif, 21944 Saudi Arabia)
Maha M. Helmi (Department of Mathematics and Statistics, College of Science, Taif University, Taif, 21944 Saudi Arabia)
Rahmatullah Ibrahim Nuruddeen (Department of Mathematics, Faculty of Physical Sciences, Federal University Dutse, Jigawa State, Nigeria, rahmatullah.n@fud.edu.ng)
Mounirah Areshi (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk, 71491 Saudi Arabia) |
| Abstract |
The current manuscript models the propagation of surface waves on a mechanically loaded,
thin, multi-layered coating half-space using the renowned asymptotic approximation method. Perfect
interfacial conditions are imposed between the composite medium’s multiple layers, in addition to boundedness conditions along the depth of the underlying half-space. Approximate equations of plane
motion and the secular equation for the propagation of Rayleigh-type waves on the governing multilayered coating substrate have been derived, utilizing the effective boundary data on the multi-interface of the medium under the long-wave approximation limit. The acquisition of an approximate elliptic-hyperbolic equation of motion, featuring a pseudo-differential operator and characterized by impulsive point loading, led to the observation of oscillatory wave behaviors in both the longitudinal
displacement and potential functions with respect to the scaled spatial-temporal variable χ. Finally,
some numerical illustrations, considering prototypical high-contrast coatings and stiff substrates,
exhibit slow oscillations of the progressing and receding fronts. Conversely, an opposite trend is noted when a soft underlying substrate is placed beneath a stiff multi-layered coating. |
| Keywords |
surface wave propagation, thin coating, multi-layered coating, hyperbolic-elliptic equation, secular equation |
| Received |
17 July 2024 | Revised |
08 September 2024 | Accepted |
30 September 2024 |
| Link to Fulltext |
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