Force driven vibrations of fractionally damped plates subjected to primary and internal resonances
Research Center on Dynamics of Solids and Structures, Voronezh State Technical University, 394006, Voronezh, Russia
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Accepted: 8 June 2019
Published online: 3 September 2019
In the present paper, nonlinear force driven vibrations of thin plates in a viscoelastic medium have been studied, when its damping features are described by the fractional derivative Kelvin-Voigt model. The motion of the plate is governed by a set of three coupled nonlinear differential equations subjected to the different conditions of the internal resonance accompanied by the external resonance, resulting in the interaction of three modes corresponding to the mutually orthogonal displacements. Nonlinear sets of resolving equations in terms of amplitudes and phase differences have been obtained. The influence of fractional order viscosity and external vertical harmonic force on the energy exchange mechanism between the coupled modes has been analyzed.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019