We analyze the influence of nonlinearities in boundary conditions on the free nonlinear vibrations of rectangular plates. The nonlinear boundary conditions for membrane forces are transformed into linear boundary conditions with the help of a stress function. Auxiliary boundary conditions that describe the absence of in-plane displacements in its clamped part are taken into account. We present the comparison of backbone curves obtained with regard for the linear and nonlinear boundary conditions.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 3, pp. 72–81, July–September, 2012.
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Breslavsky, I.D., Avramov, K.V. Influence of Nonlinearities in Boundary Conditions on the Free Vibrations of Plates Under Geometrically Nonlinear Deformation. J Math Sci 194, 213–224 (2013). https://doi.org/10.1007/s10958-013-1521-4
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DOI: https://doi.org/10.1007/s10958-013-1521-4