Group properties of equations of solid deformation mechanics with nonlocal coefficients

B. D. Annin^a, S. I. Senashov<sup>b

a</sup> Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b M. F. Reshetnev Siberian State University of Science and Technologies, Krasnoyarsk

Abstract: The problem of group classification is solved for equations describing vibrations of a nonlinear elastic plate in a gas flow. Exact solutions of these equations are presented, which can be used as benchmarks for numerical solutions.

Keywords: differential equations with nonlocal coefficients, vibrations of a nonlinear elastic plate.

UDC: 517.9

Received: 13.06.2024
Revised: 11.09.2024
Accepted: 30.09.2024

DOI: 10.15372/PMTF202415552

 English version: Journal of Applied Mechanics and Technical Physics, 2025, 66:4, 822–826

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