黏弹性传动带1:3内共振时的周期和混沌运动

研究了参数激励作用下黏弹性传动带在1:3内共振时的周期解分岔和混沌动力学. 同时考虑传动带的线性外阻尼因素和材料内阻尼因素. 首先建立了具有线性外阻尼情况下的黏弹性传动带平面运动时的非线性动力学方程, 黏弹性材料的本构关系用Kelvin模型描述. 然后考虑黏弹性传动带的横向振动问题, 利用多尺度法和Galerkin离散法得到黏弹性传动带系统在1:3内共振时的平均方程. 最后利用数值模拟方法研究了黏弹性传动带系统的周期振动和混沌动力学, 得到了系统在不同参数下的混沌运动. 数值模拟结果说明黏弹性传动带系统存在周期分岔, 概周期运动及混沌运动.

Periodic and chaotic oscillation of a parametrically excited viscoelastic moving belt with 1:3 internal resonance

In this paper, the bifurcations of periodic solutions and chaotic dynamics for a parametrically excited viscoelastic moving belt with 1:3 internal resonance are investigated for the first time. The external damping and the internal damping of the material for viscoelastic moving belt are considered simultaneously. First, the nonlinear equation of planar motion for viscoelastic moving belt with the external damping is established. The Kelvin viscoelastic model is adopted to describe the relation between the stress and strain for viscoelastic material. Then, the transverse nonlinear oscillations of viscoelastic moving belt are considered. The method of multiple scales and the Galerkin approach are applied directly to the partial differential governing equation of viscoelastic moving belt to obtain the averaged equations under the case of 1:3 internal resonance and primary parametric resonance of the nth mode. Finally, numerical simulation method is used to investigated the bifurcations of periodic solutions and chaotic dynamics for viscoelastic moving belt. The chaotic motions are found under the cases of different parameters. The results of numerical simulation demonstrate that there exist periodic, 2-periodic, 3-periodic, 5-periodic and quasiperiodic responses and chaotic motions in viscoelastic moving belt.