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Technical Brief

Dynamic Analysis of an Elevator Traveling Cable Using a Singularity-Free Beam Formulation

[+] Author and Article Information
W. Fan

Division of Dynamics and Control,
School of Astronautics,
Harbin Institute of Technology,
Harbin 150001, China;
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250

W. D. Zhu

Division of Dynamics and Control,
School of Astronautics,
Harbin Institute of Technology,
Harbin 150001, China;
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: wzhu@umbc.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 23, 2016; final manuscript received January 22, 2017; published online March 2, 2017. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 84(4), 044502 (Mar 02, 2017) (9 pages) Paper No: JAM-16-1317; doi: 10.1115/1.4035857 History: Received June 23, 2016; Revised January 22, 2017

A round elevator traveling cable is modeled using a singularity-free beam formulation. Equilibria of the traveling cable with different elevator car positions are studied. Natural frequencies and the corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by abaqus. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated and they are in good agreement with those from commercial multibody dynamics software recurdyn. Effects of vertical motion of the car on free responses of the traveling cable and those of in-plane and out-of-plane building sways on forced responses are investigated.

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References

Figures

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Fig. 1

Geometrical description of an arbitrary point P on the beam

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Fig. 2

Equilibria of traveling cables with different values of σ and H

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Fig. 3

First four in-plane mode shapes of the traveling cable; the left mode shape in each subfigure is the mode shape from abaqus and the right one is that from the current formulation

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Fig. 4

First four out-of-plane mode shapes of the traveling cable; the left mode shape in each subfigure is the mode shape from abaqus and the right one is that from the current formulation

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Fig. 5

First 11 natural frequencies of the traveling cable with different car positions

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Fig. 6

Displacements of the three particles on the traveling cable due to vertical motion ofthecar

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Fig. 7

Installation position of the elevator traveling cable in the building

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Fig. 8

Displacements of the three particles on the traveling cable due to in-plane and out-of-plane building sways

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