| 基于积分本构黏弹性带的横向非线性动力学 |
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| 引用本文： | 刘彦琦,张伟,高美娟,杨晓丽.基于积分本构黏弹性带的横向非线性动力学[J].力学学报,2008,40(3):421-432. |
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| 作者姓名： | 刘彦琦 张伟 高美娟 杨晓丽 |
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| 作者单位： | 北京工业大学机电学院 北京工业大学机电学院 北京工业大学机电学院 北京工业大学机电学院 |
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| 摘 要： | 研究了黏弹性传动带在1:1内共振时的横向非平面非线性动力学特性. 首先，利用
Hamilton原理建立了黏弹性传动带横向非平面非线性动力学方程. 然后综合应用多尺度法和
Galerkin离散法对偏微分形式的动力学方程进行摄动分析，得到了四维平均方程. 对平均方
程的稳定性进行了分析，从理论上讨论了动力系统解的稳定性变化情况. 最后数值模拟结果
表明黏弹性传动带系统存在混沌运动、概周期运动和周期运动.
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| 关 键 词： | 黏弹性传动带 非线性 横向振动 内共振 混沌 |
| 收稿时间： | 2006-12-18 |
| 修稿时间： | 2007-09-19 |
TRANSVERSE NONLINEAR NONPLANAR DYNAMICS OF AN AXIALLY MOVING VISCOELASTIC BELT WITH INTEGRAL CONSTITUTIVE LAW |
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| Liu Yanqi,Zhang Wei,Gao Meijuan,Yang Xiaoli.TRANSVERSE NONLINEAR NONPLANAR DYNAMICS OF AN AXIALLY MOVING VISCOELASTIC BELT WITH INTEGRAL CONSTITUTIVE LAW[J].chinese journal of theoretical and applied mechanics,2008,40(3):421-432. |
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| Authors: | Liu Yanqi Zhang Wei Gao Meijuan Yang Xiaoli |
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| Institution: | College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China |
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| Abstract: | In this paper, the problem of the transverse nonlinear
nonplanar oscillations of an axially moving viscoelastic belt with the
integral constitutive law are investigated in the case of 1:1 internal
resonance. The governing equations of this problem are firstly derived with
the generalized Hamilton's principle to obtain the in-plane and out-of-plane
transverse nonlinear oscillations of the axially moving viscoelastic belt
neglecting the axially deformation. Perturbation analyses are carried out on
these partial differential governing equations with the multiscale method
and the Galerkin's approach to obtain four-dimensional averaged equations
and to analyze the stabilities of the solution in the dynamic system. The
simulation results show the periodic motion, the quasi-periodic motion and
the chaotic motion in the transverse nonlinear nonplanar oscillations of the
axially moving viscoelastic belt. |
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| Keywords: | viscoelastic belt nonlinear transverse vibration internal resonance chaos |
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