### SOLUTION TO THE PROBLEM OF THERMOELASTIC VIBRATION OF A PLATE IN SPECIAL BOUNDARY CONDITIONS

Pages 31 - 36

Operating conditions of uneven non-stationary heating can cause changes in physical and mechanical properties of materials. The awareness of the value and nature of thermal stresses is needed to perform a comprehensive analysis of structural strength.

The authors provide their solution to the problem of identification of natural frequencies of vibrations of rectangular plates, whenever a thermal factor is taken into account.

In the introductory section of the paper, the authors provide the equation describing the thermoelastic vibration of a plate and set the initial and boundary conditions. Furthermore, the authors provide a frequency equation derivation for the problem that has an analytical solution available (if all edges are simply supported at zero temperature). The equation derived by the authors has no analytical solution and can be solved only numerically.

In the middle of the paper, the authors describe a method of frequency equation derivation for plates exposed to special boundary conditions, if the two opposite edges are simply supported at zero temperature, while the two other edges have arbitrary types of fixation and arbitrary thermal modes.

For this boundary condition derived as a general solution, varying fixation of the two edges makes it possible to obtain transcendental trigonometric equations reducible to algebraic frequency equations by using expending in series. Thus, the obtaining frequency equations different from the general solution becomes possible for different types of boundary conditions.

The final section of the paper covers the practical testing of the described method for the problem that has an analytical solution (all edges are simply supported at zero temperature) as solved above. An approximate equation provided in the research leads to the analytical solution that is already available.

DOI: 10.22227/1997-0935.2012.7.31 - 36

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