Nonlinear analysis of a typical nonlinear beam structure based on experimentally extracted dynamical characteristics

Abstract

Measuring nonlinear characteristics of a flexible structure is difficult and complicated since the nonlinear phenomena often exhibits several special features such as unstable vibration and bifurcation. The purpose of this paper is to propose a novel computing method for extracting dynamical characteristics of a typical nonlinear beam structure. Through comparing with the experimental data derived from modal experiments, the accuracy and feasibility of nonlinear normal modes function can be validated. Afterwards, the dimensionless dynamical equation that can indeed analyze nonlinear characteristics of the system is deduced, and the associated nonlinear frequency response is calculated based on Harmonic Balance method. According to comparisons between numerical simulations and experimental harmonic frequency response of the structure from a swept-sine experiment, the accuracy of the deduced dimensionless dynamical equation can be certified and the nonlinear analysis of the system is believed to be realized. Finally, the nonlinear attractor and bifurcation phenomena are discussed, and the stable condition is validated based on the Lorenz-like system.