Influence of pressure and density of the surrounding medium on the frequency spectrum of rectangular plates hinged along the perimeter

K. B. Sabitov, A. G. Khakimov

Mavlyutov Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences, Ufa

Abstract: The frequency spectrum and mode shapes of flexural vibrations of rectangular plates in contact with a liquid or gas are determined. An expression is derived for the distributed transverse load on a plate hinged along its contour. The plate surfaces are in contact with a medium characterized by varying density and pressure. The medium may be either compressible or incompressible. The effects of mean pressure, curvature of the mid-surface, and the added mass of the gaseous medium on the plate's bending behavior are evaluated.

Keywords: thin plate, liquid, gas, density, pressure, added mass, velocity potential, frequency spectrum, vibration mode shapes.

UDC: 533.2; 534.12

Received: 06.05.2024
Revised: 10.09.2024
Accepted: 30.09.2024

DOI: 10.15372/PMTF202415506

 English version: Journal of Applied Mechanics and Technical Physics, 2025, 66:3, 546–559

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