Abstract: In the present paper, forced nonlinear vibrations of the Uflyand-Mindlin type plate subjected to the action of compressive harmonic loading are investigated for the case when damping forces are described by the fractional derivative Kelvin-Voigt model. The equations of motion are represented by a set of five nonlinear differential equations involving two in-plane displacements, deflection, and two angles of rotation, considering rotary inertia and shear deformations. The solution is constructed by the fractional derivative expansion method, which is the generalization of the method of multiple time scales usually used for problems with nonlinear differential equations of integer order. The simultaneous internal combinational and primary resonance case has been examined, and governing nonlinear differential equations have been derived. Numerical studies have been carried out for different combinations of plate parameters, and the influence of the fractional parameter, i.e., order of the fractional derivative, has been revealed.

Keywords: Nonlinear vibrations, fractional damping, fractional derivative expansion method, combinational resonance of the difference type, Uflyand-Mindlin plate, fractional derivative Kelvin-Voigt model

Pages: 79-92