Abstract
In the present paper, the non-linear free vibrations of fractionally damped plates are investigated for the case when its equations of motion involve the rotary inertia and shear deformations via five coupled nonlinear differential equations in terms of three mutually orthogonal displacements and two angles of rotation. The damping features of the surrounding medium are described by the fractional detivative Kelvin-Voigt model. The procedure resulting in decoupling linear parts of governing equations has been proposed, what allows one to utulyze effectively the fractional derivative expansion method for solving the non-linear equations of motion. The occurrence of the internal or combinational resonances has been revealed and classified for plates of the Uflyand-Mindlin type.
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