Natural Frequencies of a Very Large–Sag Extensible Cable
Publication: Journal of Engineering Mechanics
Volume 144, Issue 2
Abstract
This technical note presents a model formulation that can be used for analyzing the in-plane free vibration behaviors of a very large–sag extensible cable supported at the same and different levels. The formulation model developed in this study is based on a variational approach, which involves the virtual strain energy because of axial stretching, the virtual work done by cable self-weight, and by the inertia forces. The coupled equations of motion in the Cartesian coordinates are obtained by taking into account the difference of Euler’s equations between equilibrium and displaced states. The Galerkin finite element method is used to obtain the mass and stiffness matrices and then the eigenvalue problem is solved. The numerical analysis results are given to demonstrate the dynamic free vibration on natural frequencies and mode shapes of various characteristics of cables from very small–sag to very large–sag cable configurations, the special case of a very large–sag cable was investigated and compared with the natural frequencies and mode shapes of the simple hanging chain.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to acknowledge the Institutional Research Capability Development Grant from Thailand Research Fund (TRF) and King Mongkut’s University of Technology Thonburi (KMUTT).
References
Casciati, S. (2016). “Human induced vibration versus cable-stay footbridge deterioration.” J. Smart Struct. Syst., 18(1), 17–29.
Chandrupatla, T. R., and Belegundu, A. D. (2012). Introduction to finite elements in engineering, Prentice-Hall, Upper Saddle River, NJ.
Chucheepsakul, S., and Huang, T. (1997). “Effect of axial deformation on natural frequencies of marine cables.” Proc., 7th Int. Offshore and Polar Engineering Conf. (ISOPE), Vol. II, Honolulu, Hawaii, 131–136.
Dan, D., Chen, Z., and Yan, X. (2014). “Closed-form formula of the transverse dynamic stiffness of a shallowly inclined taut cable.” J. Shock Vibr., 1–14.
Huang, T., and Dareing, D. W. (1969). “Frequencies of a hanging chain.” J. Acoust. Soc. Am., 45(4), 1046–1049.
Irvine, H. M. (1981). Cable structures, MIT Press, Cambridge, MA.
Irvine, H. M., and Caughey, T. K. (1974). “The linear theory of free vibrations of a suspended cable.” Proc., Royal Soc. A, 341(1626), 299–315.
Phanyasahachart, T., Athisakul, C., and Chucheepsakul, S. (2017). “Analysis of large-sag extensible catenary with free horizontal sliding at one end by variational approach.” Int. J. Struct. Stab. Dyn., 17(7), 1–17.
Rega, G. (2004a). “Nonlinear dynamics of suspended cables. Part I: Modeling and analysis.” ASME Appl. Mech. Rev., 57(6), 441–476.
Rega, G. (2004b). “Nonlinear dynamics of suspended cables. Part II: Deterministic phenomena.” ASME Appl. Mech. Rev., 57(6), 477–511.
Srinil, N., Rega, G., and Chucheepsakul, S. (2003). “Large-amplitude three-dimensional free vibrations of inclined sagged elastic cables.” J. Nonlinear Dyn., 33(2), 129–154.
Starossek, U. (1991). “Dynamic stiffness matrix of sagging cable.” J. Eng. Mech., 2815–2828.
Takahashi, K., and Konishi, Y. (1987). “Non-linear vibration of cables in three dimensions. I: Non-linear free vibrations.” J. Sound Vibr., 118(1), 69–84.
Triantafyllou, M. S., and Grinfogel, L. (1986). “Natural frequencies and modes of inclined cables.” J. Struct. Eng., 139–148.
Verbin, Y. (2015). “Boundary conditions and modes of the vertically hanging chain.” Eur. J. Phys., 36(1), 015005–0150010.
Information & Authors
Information
Published In
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 26, 2017
Accepted: Aug 8, 2017
Published online: Dec 8, 2017
Published in print: Feb 1, 2018
Discussion open until: May 8, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.