Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates




rectangular plate, free vibrations, clamped-clamped plate, Galerkin method, Voigt solution


The principally new method of selected exact solutions, SES, for plate vibration based on fundamental solutions of Voigt is suggested. In contrast to similar known methods, it employs the frequency dependent functions for both space coordinates. The sets of exact solutions which depends on some arbitrary chosen parameters are constructed. This allows to choose any number of exact solutions, while the required number of them depends on the boundary conditions which should satisfy in considered collocation points.

The efficiency of method is demonstrated for the most unfavorable case of all sides clamped rectangular plate. Nevertheless, the accuracy is quite satisfactory for first six natural frequencies even for relatively small number of collocation boundary points, and testify about big prospects as to application for complex structures, different geometries, various boundary conditions.

Additionally two variants of the Galerkin method are realized and compared. First one, employs the exponential functions, while the second one –the very popular beam functions. The calculation results show the superiority of first variant as in technical realization as in accuracy, and in further applications in structural mechanics.

Author Biographies

Igor Orynyak, Department of Applied Mathematics at National Technical University Kiev Polytechnic Institute

Professor of Department of Applied Mathematics

Julia Bai, Igor Sikorsky Kyiv Polytechnic Institute

Кафедра прикладної математики, старший викладач

Iryna Kostiushko, Department of Applied Mathematics at National Technical University Kiev Polytechnic Institute

Senior Reader of Department of Applied Mathematics


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How to Cite

I. Orynyak, J. Bai, and I. Kostiushko, “Applications of randomly selected sets of exact Voight’s solutions for vibration of thin plates”, Mech. Adv. Technol., vol. 6, no. 3, pp. 237–245, Dec. 2022.