Force driven nonlinear vibrations of a thin plate with 1:1 internal resonance in a fractional viscoelastic medium

International Conference of Young Scientists and Students "Topical Problems of Mechanical Engineering 2018"

Shitikova, M.V.^1 ; Kandu, V.V.^1

Voronezh Technical State University, Research Center on Dynamics of Solids and Structures, 20-letija Oktjabrja Street 84, Voronezh

394006, Russia^1

关键词: 1:1 internal resonances;    Comparative analysis;    Fractional derivatives;    Free and forced vibrations;    Multiple time scale;    Non-linear vibrations;    Numerical calculation;    Visco-elastic mediums;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/489/1/012043/pdf
DOI  :  10.1088/1757-899X/489/1/012043

来源: IOP

【 摘 要 】

In the present paper, force driven vibrations of a physically nonlinear plate are studied by the method of multiple time scales when the plate is subjected to the conditions of the one-to-one internal resonance. The damping features of the surrounding medium are described by the fractional derivative Kelvin-Voight model. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed. For the one-to-one 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 of free and forced vibrations are presented.