高阶模态对弹性屈曲梁混沌运动的影响

为了讨论高阶模态对混沌运动的影响，建立了横向载荷作用下弹性屈曲简支梁的非线性动力方程，将其化为常微分方程或方程组。对梁的单模态模型采用Ｍｅｌｎｉｋｏｖ函数法给出了发生混沌运动的门槛值，对梁的单模态模型和双模态模型利用时程曲线、相平面轨迹，Ｐｏｉｎｃａｒｅ映射判断是否发生混沌运动，理论和数值分析表明高阶模态对混沌运动具有很大的影响。

Effect of Higher Order Modes on Chaotic Vibration of Buckled Elastic Beams

The primary aim of this paper is to study the effect of higher order modes on the excitation threshold for the chaotic vibration of continuous system.Considered here is a buckled beam,which is simply supported and subjected to a lateral harmonic excitation.At first,the partial differential equation governing the transverse vibration of the beam is derived.Then,by means of the Galerkin approach,the partial differential equation is simplified into a single ordinary differential equation or a set of two ordinary differential equations according to the number of modes taken into account.For the single mode model of the beam,the Melnikov method is used to give the approximate excitation threshold for the occurrence of the chaotic vibration.For the single mode model and the double mode model,the forced vibration of the beam is analyzed through the use of numerical integration and the poincare section.The numerical results show that the higher order modes play an improtant role in analyzing the chaotic motion.