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Force driven vibrations of fractionally damped plates subjected to primary and internal resonances

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Abstract.

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.

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Authors and Affiliations

  1. Research Center on Dynamics of Solids and Structures, Voronezh State Technical University, 394006, Voronezh, Russia

    Marina V. Shitikova & Vladimir Kandu

Authors
  1. Marina V. Shitikova
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  2. Vladimir Kandu
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Correspondence to Marina V. Shitikova.

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Shitikova, M.V., Kandu, V. Force driven vibrations of fractionally damped plates subjected to primary and internal resonances. Eur. Phys. J. Plus 134, 423 (2019). https://doi.org/10.1140/epjp/i2019-12812-x

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  • DOI: https://doi.org/10.1140/epjp/i2019-12812-x

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