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TECHNICAL PAPERS

A Non-Incremental Nonlinear Finite Element Solution for Cable Problems

[+] Author and Article Information
Hiroyuki Sugiyama

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60607

Aki M. Mikkola

Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53851 Lappeenranta, Finland

Ahmed A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607

J. Mech. Des 125(4), 746-756 (Jan 22, 2004) (11 pages) doi:10.1115/1.1631569 History: Received January 01, 2002; Revised March 01, 2003; Online January 22, 2004
Copyright © 2003 by ASME
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References

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Saxon,  D. S., and Cahn,  A. S., 1953, “Modes of Vibration of a Suspended Chain,” Q. J. Mech. Appl. Math., 6, pp. 273–285.
Irvine,  H. M., and Caughey,  T. K., 1974, “The Linear Theory of Free Vibration of a Suspended Cable,” Proc. R. Soc. London, Ser. A, 341, pp. 299–315.
Irvine, H. M., 1981, Cable Structures, MIT Press.
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Henghold,  W. M., and Russell,  J. J., 1976, “Equilibrium and Natural Frequencies of Cable Structures (A Nonlinear Finite Element Approach),” Comput. Struct., 6, pp. 267–271.
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Figures

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Nondimensional natural frequencies for small sagged cable 5: a. the first symmetric mode, b. the first antisymmetric mode, c. the second symmetric mode, d. the second antisymmetric mode.
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Beam element in the absolute nodal coordinate formulation
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Sagged cable subjected to ground excitation
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Transverse deflection at mid-span (a=1.0 m/s2)
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Transverse deflection at mid-span (a=10.0 m/s2)
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Deformed shapes of the falling cable pendulum
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Vertical displacement of cable tip
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Energy balance: -▪-, kinetic energy; -•-, strain energy; -▴-, potential energy; -○-, total energy.
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Element coordinate system
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Mode shapes and natural frequencies: (a) linearized ANCF, •, (b) analytical solution 5; –.
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The cable system under investigation
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Motion simulation (ω=18.0 rad/s)

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