Analysis of forced vibrations

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International Journal for Computational Civil and Structural Engineering. International Journal for Computational Civil and Structural Engineering, 15(3) 131-148 (2019).
In the present paper, the force driven dynamic response of a nonlinear plate embedded in a viscoelastic medium, damping features of which are described by the Kelvin-Voigt fractional derivative model, is studied. The motion of the plate is described by three coupled nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal combinational resonance accompanied by the external resonance, resulting in the interaction of three modes corresponding to the mutually orthogonal displacements. A comparative analysis of numerical calculations for the cases of free and forced vibrations has been carried out.
Recently the interest to nonlinear dynamic response of viscoelastic plates or elastic plates vibrating in a viscoelastic surrounding medium has been greatly renewed due to the appearance of advanced materials exhibiting nonlinear behaviour, and a comprehensive review in the field, including experimental results, could be found in (1-6).
Nonlinear vibrations of thin plates, Interaction of internal and external resonances, Fractional derivative viscoelastic surrounding medium, Combinational internal resonance
Shitikova, M.V., Kandu, V.V. (2019). Analysis of forced vibrations of nonlinear plates in a viscoelastic medium under the conditions of the different combinational internal resonances. DOI:10.22337/2587-9618-2019-15-3-131-148