Nonlinear Vibration Analysis of Flexible Hoisting Rope with Time-Varying Length
Nonlinear Vibration Analysis of Flexible Hoisting Rope with Time-Varying Length
复制标题
时变长度柔性提升绳非线性振动分析
DOI：
10.20855/ijav.2015.20.3380
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Ming Zhu
中科院分区：
文献类型：
--
作者：
Ji-hu Bao;Peng Zhang;Chang-ming Zhu;Ming Zhu
研究了具有时变长度和轴向速度的柔性提升钢丝绳的非线性振动。柔性提升绳被建模为在其下端连接有刚性体的拉紧平移绳。本文提出了一种系统地推导具有时变长度和轴向速度的柔性提升钢丝绳系统模型的方法。采用扩展的汉密尔顿原理，考虑钢丝绳的轴向运动和弯曲变形的耦合，建立了钢丝绳的控制方程。所导出的控制方程是具有时变系数的非线性偏微分方程。采用Galerkin方法和四阶RungeKutta方法对所得方程进行了数值分析。根据李雅普诺夫稳定性理论，分析了柔性提升钢丝绳的动态稳定性。以电梯提升系统的运动为例，说明了所提出的数学模型。仿真结果表明，柔性提升管柱的动态运动在下降过程中是稳定的，而在上升过程中是不稳定的。所提出的系统的动力稳定性分析方法，可为柔性提升系统的动力控制研究提供参考。
The nonlinear vibration of a flexible hoisting rope with time-varying length and axial velocity is investigated. The flexible hoisting rope is modeled as a taut translating string with a rigid body attached at its low end. A systematic procedure for deriving the system model of a flexible hoisting rope with time-varying length and axial velocity is presented. The governing equations were developed by employing the extended Hamilton’s principle considering coupling of axial movement and flexural deformation of the rope. The derived governing equations are nonlinear partial differential equations(PDEs) with time-varying coefficients. The Galerkin’s method and the 4th RungeKutta method were employed to numerically analyze the resulting equations. Further, the dynamic stability of the flexible hoisting rope was investigated according to the Lyapunov stability theory. The motions of an elevator hoisting system were presented to illustrate the proposed mathematical models. The results of simulation show that the dynamic motions of the flexible hoisting string are stable during downward movement but are unstable during upward movement. The proposed systematic procedures in analyzing the dynamic stability can facilitate further development in dynamic control of the flexible hoisting system in practice.
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DOI：
10.1007/s00526-007-0094-9
发表时间：
2000
影响因子：
2.1
作者：
H. Brezis;Jean Van Schaftingen
通讯作者：
H. Brezis;Jean Van Schaftingen
DOI：
10.1299/kikaic.74.31
发表时间：
2008
期刊：
Transactions of the Japan Society of Mechanical Engineers. C
影响因子：
--
作者：
H. Kimura;Tomoki Iijima;S. Matsuo;Y. Fujita
通讯作者：
H. Kimura;Tomoki Iijima;S. Matsuo;Y. Fujita
影响因子：
4.7
作者：
R. Chi;H. Shu
通讯作者：
R. Chi;H. Shu
DOI：
10.20855/ijav.2000.5.357
发表时间：
2000
期刊：
--
影响因子：
--
作者：
S. Kaczmarczyk;W. Ostachowicz
通讯作者：
S. Kaczmarczyk;W. Ostachowicz
DOI：
--
发表时间：
2008
期刊：
Journal of Shanghai Jiaotong University
影响因子：
--
作者：
Liang-juan Zhang
通讯作者：
Liang-juan Zhang