Modeling and Analysis of Rope Transverse Vibration for Flexible Hoisting Systems with TimeVarying Length

Abstract

Abstract: Transverse vibration of rope with timevarying length was investigated considering the continuum medium mechanics and the effect of the geometrically non-linear kinematics of deformation. The governing equations were developed employing the Hamiltons principle. The Galerkins method is used to discretize the governing equations. The motions of traction elevator hoisting systems were illustrated to evaluate the proposed mathematical models and solution method. The results of simulation show that the modeling methods considering the continuum medium mechanics can well represent the transverse vibration of hoisting rope systems with timevarying length.

Key words: flexible hoisting system, transverse vibration, rope, traction elevator

CLC Number:

TB 123

BAO Ji-Hu-a, ZHANG Peng-a, b , ZHU Chang-Ming-b. Modeling and Analysis of Rope Transverse Vibration for Flexible Hoisting Systems with TimeVarying Length[J]. Journal of Shanghai Jiaotong University, 2012, 46(03): 341-345.

References

［1］Hiroyuki K, Hiroaki I, Toshiaki N. Vibration analy

sis of elevator rope(2nd report, forced vibration of rope with damping)［J］. Journal of System Design and Dynamics, 2008, 2(2):540549.
［2］Hiroyuki K, Tomoki I, Shigenori M, et al. Vibration analysis of elevator rope(Comparison between experimental results and calculated results)［J］. Journal of System Design and Dynamics, 2009, 3(3):420428.
［3］杜小强,梅德庆,陈子辰.高速曳引电梯时变元模型与水平振动响应分析［J］.浙江大学学报(工学版), 2009, 43(1):148152.
DU Xiaoqiang, Mei Deqing, CHEN Zichen. Timevary element model highspeed traction elevator and its horizontal vibration response analysis［J］. Journal of Zhejiang University (Engineering Science), 2009, 43(1):148152.
［4］Lee S Y, Lee M. A new wave technique for free vibration of a string with timevarying length［J］. Journal of Applied Mechanics, 2002, 69(1):8387.
［5］Wickert J A, Mote Jr C D. Classical vibration analysis of axially moving continua［J］. Journal of Applied Mechanics, 1990, 57(9):738744.
［6］Kaczmarczyk S, Ostachowicz W. Transient vibration phenomena in deep mine hoisting cables. Part1:Mathematical model［J］. Journal of Sound and Vibration, 2003, 262:219244.
［7］Zhu W D, Ni J. Energetics and stability of translating media with an arbitrarily varying length［J］. Journal of Vibration and Acoustics, 2000, 122:295304.
［8］陆佑方. 柔性多体系统动力学［M］. 北京:高等教育出版社, 1996:3033.
［9］朗道Л.Д.,栗弗席兹 E.M..连续介质力学(第三册)［M］. 彭旭麟译. 北京:人民教育出版社, 1962:768781.
［10］王文亮, 张文, 罗惟德,等. 结构动力学［M］. 上海:复旦大学出版社, 1993:127135.
［11］张鹏, 朱昌明, 张梁娟. 变长度柔性提升系统纵向横向受迫耦合振动分析［J］. 工程力学, 2008, 25(12):202207.
ZHANG Peng, ZHU Changming, ZHANG Liangjuan. Analysis of forced coupled longitudinaltransverse vibration of flexible hoisting systems with varying length［J］. Engineering Mechanics, 2008, 25(12):202207.

[1]	CHEN Zhenwei, LU Jialin, CHEN Xupeng. Effect of Tip Skew Coupled Rake on Hydrodynamic Performance of Kappel Propellers [J]. Journal of Shanghai Jiao Tong University, 2026, 60(3): 399-407.
[2]	YU Kai, CHENG Chen, SHI Guangyu, LIU Dengcheng, WANG Chao. Numerical Study on Cavitation Characteristics of Propeller Under Oblique Flow Conditions [J]. Journal of Shanghai Jiao Tong University, 2026, 60(3): 408-417.
[3]	ZHAO Xuan, ZHAO Qi, ZHANG Daxu, ZHANG Peifu. Effects of Polymer Matrices on Interlaminar Shear Strength of GFRP Rebars in Seawater Sea-Sand Concrete Environment [J]. Journal of Shanghai Jiao Tong University, 2026, 60(3): 452-462.
[4]	TU Tiangang, YANG Weitao, YANG Qi, XU Bin. Damping Characteristics of Fe-Mn Alloy and Its Helical Spring [J]. Journal of Shanghai Jiao Tong University, 2025, 59(8): 1192-1202.
[5]	YAN He, ZHU Xingyue, HOU Zhangli, WANG Weijun, ZHANG Zhinan. Design and Motion Modeling of a Small-Scale Lunar Jumping Robot [J]. Journal of Shanghai Jiao Tong University, 2025, 59(8): 1169-1180.
[6]	SUN Bowen, YANG Jianhua, LI Baofeng, LI Shangyuan, WANG Liang, XU Zhongqi. Wire Rope Inspection Robots: A Review [J]. J Shanghai Jiaotong Univ Sci, 2025, 30(6): 1144-1161.
[7]	ZHAO Xiangtang, ZHAO Zhigang, WEI Qizhe, SU Cheng. Dynamic Analysis and Trajectory Solution of Multi-Robot Coordinated Towing System [J]. J Shanghai Jiaotong Univ Sci, 2025, 30(6): 1134-1143.
[8]	ZHANG Xue, LU Yunchao, HAN Yuanfei, LE Jianwen, HUANG Guangfa, LYU Weijie. Laser Additive Manufacturing of Discontinuously Reinforced Titanium Matrix Composites： Controlling of Microstructure-Property and Aerospace Applications [J]. Air & Space Defense, 2025, 8(5): 31-46.
[9]	CAO Huan, CAI Ao, CHEN Yangyu, ZUO Wenkang, CHEN Mantai. Behavior of High Strength Steel Butt Joints at Arctic Low Temperatures [J]. Journal of Shanghai Jiao Tong University, 2025, 59(4): 533-540.
[10]	LI Bing. Jacket Horizontal Non-Skidway Construction and SPMT Loadout Technology [J]. Ocean Engineering Equipment and Technology, 2025, 12(4): 32-37.
[11]	ZHANG Shutian, CHEN Zehan, TIAN Yutao, et al. Structural Design of an Offshore Floating Base under a Modular Concept [J]. Ocean Engineering Equipment and Technology, 2025, 12(4): 18-31.
[12]	Xu Qingyu, Hai Jizhe, Shan Chunlong, Li Haijie. Mechanical and Permeability Properties of Radial-Gradient Bone Scaffolds Developed by Voronoi Tessellation for Bone Tissue Engineering [J]. J Shanghai Jiaotong Univ Sci, 2025, 30(3): 433-445.
[13]	Wang Baomin, Ding Hewei, Teng Fei, Liu Hongqin. Damage Detection of X-ray Image of Conveyor Belts with Steel Rope Cores Based on Improved FCOS Algorithm [J]. J Shanghai Jiaotong Univ Sci, 2025, 30(2): 309-318.
[14]	ZENG Jingbo, WANG Huoping. Effect of Heat Input on Microstructure and Mechanical Properties of FCAW-G Joints of Extra High Strength Steel [J]. Ocean Engineering Equipment and Technology, 2025, 12(1): 67-73.
[15]	LI Jinfeng, CHEN Wuguang, ZHANG Zhengchuan, XU Yongliang, LI Kaiying, YIN Junlian, WANG Dezhong. Measurement of Gas-Liquid Two-Phase Flow in Draft Tube [J]. Journal of Shanghai Jiao Tong University, 2024, 58(8): 1188-1200.