Vol. 16, No. 4, 2021

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Explicit model for bending edge wave on an elastic orthotropic plate supported by the Winkler–Fuss foundation

Saad N. Althobaiti, Anatolij Nikonov and Danila Prikazchikov

Vol. 16 (2021), No. 4, 543–554

The paper is concerned with a bending edge wave on a thin orthotropic elastic plate resting on a Winkler–Fuss foundation. The main focus of the contribution is on derivation of a specialised reduced model accounting for the contribution of the bending edge wave to the overall dynamic response, allowing simplified analysis for a number of dynamic problems. The developed formulation includes an elliptic equation associated with decay over the interior, and a beam-like equation on the edge governing wave propagation accounting for both bending moment and modified shear force excitation, thus highlighting a dual parabolic-elliptic nature of the bending edge wave. A model example illustrates the benefits of the approach.

elastic, plate, bending, edge wave, explicit model
Received: 11 May 2021
Revised: 27 June 2021
Accepted: 2 July 2021
Published: 9 November 2021
Saad N. Althobaiti
Department of Science and Technology
Ranyah University College, Taif University
Taif 21944
Saudi Arabia
Anatolij Nikonov
Department of Mechanics, Design and Computer Engineering
Faculty of Industrial Engineering Novo mesto
8000 Novo mesto
Danila Prikazchikov
School of Computing and Mathematics
Keele University
Keele, ST5 5BG
United Kingdom
Faculty of Mechanics and Mathematics
al-Farabi Kazakh National University