粘弹性传动带的分岔特性和混沌振动分析

研究了粘弹性传动带横向振动的分岔特性和混沌动力学行为．将传动带视为沿轴向运动的抗弯刚度较 小的粘弹性梁模型，同时考虑变形的几何非线性和材料的非线性因素，运用弹性力学方法建立了其横向振动 的偏微分方程，利用 Galerkin 方法得到了时空坐标解耦的二阶非线性动力学方程，重点探讨了带速波动对系统 动态特性的影响．采用数值方法对系统的运动响应进行仿真，分岔图和 Poincaré图表明：随着平均带速和波动 幅值的变化，系统出现周期振动和混沌振动，倍周期分岔是产生混沌振动的途径．

Analysis of bifurcation and chaotic motion on transmission visco elastic belts

The bifurcation behaviors and chaotic vibrations of transmission visco elastic belts were investigated. An improved model of axially moving visco elastic beam with small stiffness was introduced; the nonlinear effects of deflection and material were considered simultaneously, the partial differential dynamical equations for the visco-elastic belt were established using elastic mechanics method. The method of Galerkin approach was applied to obtain the second order nonlinear equations,which decoupled in time and space coordinates. The effect of the velocity perturbation of the belts was discussed emphatically. Numerical simulation method was used to yield the response of the system; the bifurcation figure and Poincaré map show that the belts may undergo periodic and chaotic motions around different equilibrium in certain parameter regions, and the chaotic motion will occur through period double bifurcation.