轴向行进带钢的非线性振动分析

摘要

The dynamic behaviour of an axially moving strip is complicated when loaded by lateral forces. In this thesis, a model of axially moving strip with the period lateral loads is developed. The governing partial differential equation of motion is derived through the Hamilton's principle and discretized using the Galerkin approach. Through numerical simulation of the ordinary differential equation, various vibration forms of moving strips are simulated under different amplitudes of excitations. With the help of Poincare Mapping, the phenomenon of bifurcation during the vibration of moving strips is analysed. Moveover, the chaotic vibration, which should be paid attention to during producing process, is discovered under the condition of improved exciton amplitude.%　　针对轴向行进带钢在受到横向激励扰动时表现出的复杂振动形式，建立轴向行进带钢的受迫振动模型，通过Hamilton原理导出运动学方程，采用Galerkin法将控制方程离散化，得到常微分形式的控制方程。对控制方程进行数值模拟，仿真出带钢在不同激励幅值下的振动形式。通过庞加莱截面映射方法对带钢振动中的分岔现象作出分析，得到在增大激励幅值情况下带钢的混沌振动规律。