Abstract
In the present paper, the dynamic behaviour of a nonlinear plate embedded into a fractional derivative viscoelastic medium is studied by the generalized method of multiple time scales when the plate is subjected to the conditions of the one-to-one-to-one internal resonance. Damping features of the surrounding medium are defined by the fractional derivative Kelvin-Voight model with a fractional parameter changing from zero to one. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed. For the 1:1:1 internal resonance, the nonlinear set of resolving equations in terms of amplitudes and phase differences has been obtained, and a comparative analysis of numerical calculations for free and forced vibrations are presented.
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