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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2024-6pp.3375-3389

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K.B. Sabitov and A.G. Khakimov, "Determination of the Spectrum of Frequencies and Vibrations of a Rectangular Plate, Mobily Employed Around the Edge, in Different Media," Mech. Solids. 59 (6), 3375-3389 (2024)
Year 2024 Volume 59 Number 6 Pages 3375-3389
DOI 10.1134/S002565442460435X
Title Determination of the Spectrum of Frequencies and Vibrations of a Rectangular Plate, Mobily Employed Around the Edge, in Different Media
Author(s) K.B. Sabitov (Mavlyutov Institute of Mechanics UFRC RAS, Ufa, 450054 Russia, sabitov_fmf@mail.ru)
A.G. Khakimov (Mavlyutov Institute of Mechanics UFRC RAS, Ufa, 450054 Russia, hakimov@anrb.ru)
Abstract The spectrum of frequencies and shapes of bending vibrations of a rectangular plate in contact with a liquid or gas are determined. A derivation of the expression for the distributed transverse load on a plate movably embedded along the contour is given. The surfaces of the plate are in contact with media of different densities and pressures. The medium can be compressible during surface deformation and incompressible. The influence on the bending of the interaction of average pressure and changes in the curvature of the middle surface, as well as the added mass of the gaseous medium, is determined.
Keywords thin plate, liquid, gas, density, pressure, added mass, velocity potential, frequency spectrum, natural oscillation modes
Received 19 June 2024Revised 29 July 2024Accepted 30 July 2024
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