Analysis of thin nonlinear plates' forced vibrations in a viscoelastic medium under the conditions of the additive combinational internal resonance

7th International Symposium Actual Problems of Computational Simulation in Civil Engineering

土木建筑工程;计算机科学

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

Voronezh State Technical University, 20-letija Oktjabrja st. 84, Voronezh

394006, Russia^1

关键词: Comparative analysis;    Coupled nonlinear differential equations;    Displacement function;    Free and forced vibrations;    Kelvin-Voigt fractional derivative model;    Multiple scales methods;    Numerical calculation;    Visco-elastic mediums;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/456/1/012047/pdf
DOI  :  10.1088/1757-899X/456/1/012047

来源: IOP

【 摘 要 】

The force driven dynamic response of a nonlinear plate embedded in a viscoelastic medium, damping features described by the Kelvin-Voigt fractional derivative model, is studied in the present paper. 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 three modes corresponding interaction to the mutually orthogonal displacements. The displacement functions are determined in terms of linear vibrations' eigenfunctions. The solution of motion nonlinear governing equations was obtained by the utilization of the multiple scales method, so doing the amplitude functions are expanded into power series in terms of the small parameter and depend on different time scales. The influence of viscosity on the energy exchange mechanism between interacting modes was analyzed. A comparative analysis of numerical calculations for the free and forced vibrations cases was carried out.