Bifurcation and Chaotic Motion of an Elastic Plate of Large Deflection Under Parametric Excitation

Abstract

The dynamic behavior of a nonlinear elastic rectangular plate of large deflection subjected to harmonic excitation is investigated. Using the Galerkin principle, a double mode model is established for the plate. The stability and bifurcation behavior of the plate is studied in detail for various loading conditions and system parameters. A set of autonomous equations is derived with the method of averaging. The bifurcation behavior is examined on the basis of the autonomous equations, and the results of theoretical bifurcation analysis are numerically verified. The chaotic response of the plate to the external excitation is also investigated. The governing equations of single as well as double modes are established and the comparison between the single and double mode models is carried out. The applicable conditions of the single mode method are provided. The results obtained show that the single mode approach usually used may lead to incorrect conclusions under certain conditions.