A nonlinear, planar model of a slack cable with bending stiffness and arbitrarily moving ends is developed. The model uses the slope angle of the centroid line of the cable to describe the motion of the cable, and the resulting integropartial differential equation with constraints is derived using Hamilton’s principle. A new method is developed to obtain the spatially discretized equations, and the Baumgarte stabilization procedure is used to solve the resulting differential-algebraic equations. The model can be used to calculate the equilibria and corresponding free vibration characteristics of the cable, as well as the dynamic response of the cable under arbitrarily moving ends. The results for an equilibrium and free vibration characteristics around the equilibrium are experimentally validated on a laboratory steel band. The methodology is applied to elevator traveling and compensation cables. It is found that a vertical motion of the car can introduce a horizontal vibration of a traveling or compensation cable. The results presented are verified by a commercial finite element software. The current method is shown to be more efficient than the finite element method as it uses a much smaller number of elements to reach the same accuracy. Some other interesting features include the condition for a traveling or compensation cable equilibrium to be closest to a natural loop and a direct proof that the catenary solution is unique.

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July 2011

Research Papers

# A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables

C. Xiao

C. Xiao

Visiting Graduate Research Assistant

Department of Mechanical Engineering,

chuangx@umbc.edu
University of Maryland

, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250
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W. D. Zhu
Professor

H. Ren
Graduate Research Assistant

C. Xiao
Visiting Graduate Research Assistant

Department of Mechanical Engineering,

University of Maryland

, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250chuangx@umbc.edu

*J. Appl. Mech*. Jul 2011, 78(4): 041017 (13 pages)

**Published Online:**April 15, 2011

Article history

Received:

August 26, 2009

Revised:

December 27, 2010

Posted:

January 4, 2011

Published:

April 15, 2011

Online:

April 15, 2011

Citation

Zhu, W. D., Ren, H., and Xiao, C. (April 15, 2011). "A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables." ASME. *J. Appl. Mech*. July 2011; 78(4): 041017. https://doi.org/10.1115/1.4003348

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