We propose a numerical-analytic method for the investigation of parametric vibrations of the plates under the action of static and periodic loads applied in the middle plane. The method is used for the equations of motion of plates obtained within the framework of the classical theory. The developed approach is based on the application of the theory of R-functions and variational methods, which enables us to study plates of arbitrary geometric shapes with various boundary conditions. According to the proposed approach, we first find the subcritical state of the plate if it is not homogeneous. To construct the zones of dynamic instability, we use the method proposed by Bolotin. The results obtained with the help of the developed approach are compared with the available data. We solve a number of new problems for multilayer plates of complex geometric shapes with holes.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 2, pp. 136–150, April–June, 2013.
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Kurpa, L.V., Mazur, O.S. & Tkachenko, V.V. Parametric Vibration of Multilayer Plates of Complex Shape. J Math Sci 203, 165–184 (2014). https://doi.org/10.1007/s10958-014-2098-2
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DOI: https://doi.org/10.1007/s10958-014-2098-2