Higher-Dimensional Periodic and Chaotic oscillations for Viscoelastic Moving Belt with Multiple Internal resonances
Higher-Dimensional Periodic and Chaotic oscillations for Viscoelastic Moving Belt with Multiple Internal resonances
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DOI：
10.1142/s0218127407017963
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发表时间：
2007-05
期刊：
影响因子：
--
通讯作者：
W. Zhang;C. Song
中科院分区：
文献类型：
--
作者：
W. Zhang;C. Song
本文首次研究了具有多个内共振的参数激励粘弹性运动带的高维周期混沌振动问题。同时考虑了粘弹性移动带材料的外阻尼和内阻尼。首先，给出了带外阻尼的粘弹性运动带平面运动的非线性控制方程。然后，考虑粘弹性运动带的横向非线性振动。将多尺度法和伽辽金方法直接应用于粘弹性运动带的运动控制偏微分方程，得到了一阶、二阶、三阶和四阶内共振为1:2:3:4时的八维平均方程和一阶模态的主参数共振。最后，采用数值方法研究粘弹性运动带的高维周期运动和混沌运动。数值模拟结果表明，粘弹性运动带存在周期、周期2、周期4、多周期和混沌运动。通过数值模拟观察了粘弹性运动带的多脉冲混沌运动。
In this paper, higher-dimensional periodic and chaotic oscillations for a parametrically excited viscoelastic moving belt with multiple internal resonances are investigated for the first time. The external damping and internal damping of the material for the viscoelastic moving belt are considered simultaneously. First, the nonlinear governing equation of planar motion for the viscoelastic moving belt with the external damping is given. Then, the transverse nonlinear oscillations of the viscoelastic moving belt are considered. The method of multiple scales and the Galerkin approach are applied directly to the governing partial differential equation of motion for the viscoelastic moving belt to obtain an eight-dimensional averaged equation for the case of 1:2:3:4 internal resonances for the first-, the second-, the third- and the fourth-order modes and primary parametric resonance of the first-order mode. Finally, numerical method is used to investigate higher-dimensional periodic and chaotic motions of the viscoelastic moving belt. The results of numerical simulation demonstrate that there exist the period, period 2, period 4, multiple period and chaotic motions of the viscoelastic moving belt. The multipulse chaotic motions of the viscoelastic moving belt are observed from numerical simulations.