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Mathematical Models and Computer Simulations

Erschienen in:

01.12.2023

Modeling the Elastic-Diffusion Vibrations of a Hinged Timoshenko Plate under the Action of a Distributed Surface Load

verfasst von: N. V. Grigorevskiy, A. V. Zemskov, A. V. Malashkin

Erschienen in: Mathematical Models and Computer Simulations | Sonderheft 1/2023

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Abstract

We consider the unsteady problem of bending a homogeneous orthotropic hinged Timoshenko elastic-diffusion plate under the action of a mechanical load distributed over the surface. The initial mathematical formulation of the problem includes the system of elastic-diffusion equations for a continuum, which takes into account the finite propagation velocity of diffusion perturbations. The equations of unsteady elastic-diffusion vibrations of the plate are obtained from the equations for a continuum using the generalized principle of virtual displacements and hypotheses of Timoshenko’s theory. The solution is sought using the Laplace transform and expansion into Fourier series. The originals are found analytically using residues and tables of operational calculus.

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Titel: Modeling the Elastic-Diffusion Vibrations of a Hinged Timoshenko Plate under the Action of a Distributed Surface Load
verfasst von: N. V. Grigorevskiy
A. V. Zemskov
A. V. Malashkin
Publikationsdatum: 01.12.2023
Verlag: Pleiades Publishing
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe Sonderheft 1/2023
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048223070050

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