Abstract
We study transverse vibrations of an inhomogeneous circular thin plate in this work. Using the perturbation method, asymptotic formulas are obtained for free-vibration frequencies of a plate whose thickness and Young’s modulus linearly depend on radius. The effect of the boundary conditions on frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For lower frequencies of the plate, the asymptotic results are compared with the results of analysis by finite elements.
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Funding
This work was financially supported in part by the Russian Foundation for Basic Research (grant nos. 18-01-00832-a and 19-01-00208-a).
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Translated by L. Kartvelishvili
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Vasiliev, G.P., Smirnov, A.L. Free Vibration Frequencies of a Circular Thin Plate with Variable Parameters. Vestnik St.Petersb. Univ.Math. 53, 351–357 (2020). https://doi.org/10.1134/S1063454120030140
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DOI: https://doi.org/10.1134/S1063454120030140