Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Starovoitov E. I., Leonenko D. V. Forced oscillations of a three-layer plate in an unsteady temperature field. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 1, pp. 123-137. DOI: 10.18500/1816-9791-2024-24-1-123-137, EDN: TMUGDP

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.03.2024
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
539.374
DOI: 
10.18500/1816-9791-2024-24-1-123-137
EDN: 
TMUGDP

Forced oscillations of a three-layer plate in an unsteady temperature field

Autors: 
Starovoitov Eduard Ivanovich, Belarusian State University of Transport
Leonenko Denis V., Belarusian State University of Transport
Abstract: 

The effect of a constant intensity heat flux on forced oscillations of a circular three-layer plate with an asymmetric thickness is investigated. The plate is thermally insulated along the contour and the lower plane. An approximate solution of the thermal conductivity problem was used, obtained by averaging the thermophysical parameters of the materials of the layers over the thickness of the package. According to the Neumann hypothesis, free plate oscillations caused by an instantaneous drop in heat flow are summed up with forced oscillations from the power load. The deformation of the plate package corresponds to the polyline hypothesis. In relatively thin outer bearing layers, Kirchhoff's hypotheses are valid. In sufficiently thick incompressible filler, the deformed normal retains straightness and length, but rotates by an additional angle. The formulation of the corresponding initial boundary value problem includes the equations of motion obtained using the d'Alembert principle and the variational Lagrange method. The initial conditions are assumed to be homogeneous, the contour of the plate is pivotally supported. The analytical solution of an inhomogeneous system of partial differential equations is obtained using the method of expansion into a series according to a system of proper orthonormal functions. As a result, analytical expressions are written out for three desired functions – plate deflection, shear and radial displacement in the filler. An example of oscillations under the action of an instantaneously applied uniformly distributed load is considered. A numerical parametric analysis of the natural oscillation frequencies and the resulting solution depending on the intensity of the heat flux for a plate with layers of titanium alloy, fluoroplast-4, and duralumin is given.

Key words: 
three-layer circular plate
forced oscillations
unstable temperature field
Acknowledgments: 
The was supported by the Belarusian Republican Foundation for Fundamental Research (project No. T22UZB-015).
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Received: 
28.11.2022
Accepted: 
16.01.2023
Published: 
01.03.2024
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