Determination of the spectrum of frequencies and vibrations of a rectangular plate, mobily employed around the edge, in different environments

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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.

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About the authors

K. B. Sabitov

Mavlyutov Institute of Mechanics

Author for correspondence.
Email: sabitov_fmf@mail.ru
Russian Federation, Ufa

A. G. Khakimov

Mavlyutov Institute of Mechanics

Email: hakimov@anrb.ru
Russian Federation, Ufa

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Supplementary files

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2. Fig. 1. Elements dx and dy of the middle surface of a curved plate.

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3. Fig. 2. Dependence of the first frequency of bending vibrations of the plate f11 (Hz) on the pressure p2 (MPa) for the pressure p1 = 0.5 MPa: (a) for different gases: = 0.1785 (helium), 1.2928 (air), 1.9768 (carbon dioxide) kg/m3 (dotted, dashed, solid lines, respectively); (b) according to the formulas for incompressible (2.25) and compressible (3.17) liquids for carbon dioxide = 1.9768 kg/m3 (solid, dotted lines, respectively).

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4. Fig. 3. Dependence of the second frequency of bending vibrations of the plate f22 (Hz) on the pressure p2 (MPa) for the pressure p1 = 0.5 MPa: (a) for different gases: = 0.1785 (helium), 1.2928 (air), 1.9768 (carbon dioxide) kg/m3 (dotted, dashed, solid lines, respectively); (b) according to the formulas for incompressible (2.25) and compressible (3.17) liquids for carbon dioxide = 1.9768 kg/m3 (solid, dotted lines, respectively).

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