粘弹性轴向运动梁的非线性动力学行为

Nonlinear Dynamical Behaviors of an Axially Moving Visco-Elastic Beam

本文研究了带有小脉动的轴向运动粘弹性梁的分岔及混沌现象。建立了系统的动力学模型。通过二阶Galerkin截断,把描述系统运动的偏微分方程离散化。利用数值方法分别分析了几种运动脉动频率时,梁随轴向运动脉动幅值,平均速度及粘弹性系数等几个参数变化时的运动分岔行为。利用Lyapunov指数识别系统的动力学行为,区分准周期振动和混沌运动。

Bifurcation and chaos of an axially moving viscoelastic beam were investigated. The 2-term Galerkin truncation was employed to simplify the partial differential equation that governs the transverse motion of the beam into a set of ordinary differential equations. The bifurcation diagrams were present in the case that the transport speed, the amplitude of the periodic perturbation or the dynamic viscosity was varied respectively while the frequency of the axially moving speed fixed at three different numbers. The dynamical behaviors were numerically identified based on the Poincare maps. Numerical simulations indicate that the periodic, quasi-periodic and chaotic motions occur in the transverse vibrations of the axially moving viscoelastic beam.