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Description of plates with matrix Klein – Gordon equation
- Authors: Kniazeva K.S1, Shelest E.L.1, Shanin A.V.1
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Affiliations:
- Lomonosov Moscow state university
- Issue: Vol 71, No 5 (2025)
- Pages: 625–632
- Section: КЛАССИЧЕСКИЕ ПРОБЛЕМЫ ЛИНЕЙНОЙ АКУСТИКИ И ТЕОРИИ ВОЛН
- URL: https://ogarev-online.ru/0320-7919/article/view/376001
- DOI: https://doi.org/10.7868/S3034500625050015
- ID: 376001
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Abstract
Matrix Klein–Gordon equation (MKGE) describes waveguides with discrete structure of their cross-section. It can be also considered as a model of a continuous waveguide obtained in the result of application of the waveguide Finite Element Method. In the current work we study applicability of MKGE to flexural vibrations of a thin plate. The question is not trivial since MKGE contains time and coordinate derivatives up to the second order, while the plate’s vibrations are obeyed to an equation with the fourth order coordinate derivative. Here we derive MKGE of different dimensions for the plate. We show that linear approximation of the displacements in the plate across its width leads to an overestimation of the plate’s rigidity, while more complicated models lead to the right values.
About the authors
K. S Kniazeva
Lomonosov Moscow state university
Email: knyazevaks05@gmail.com
Physical Faculty Moscow, Russia
E. L. Shelest
Lomonosov Moscow state universityPhysical Faculty Moscow, Russia
A. V. Shanin
Lomonosov Moscow state universityPhysical Faculty Moscow, Russia
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