Unified Finite Difference Formulation for Free Vibration of Cables
Publication: Journal of Structural Engineering
Volume 124, Issue 11
Abstract
In this paper, a finite difference formulation for vibration analysis of structural cables is introduced. This formulation incorporates into a unified solution the effects of the bending stiffness of cable and its sag-extensibility characteristics and provides a tool for accurate determination of vibration mode shapes and frequencies. Various cable-end conditions, variable cross sections, and intermediate springs and/or dampers are taken into account. Using a nondimensional form of this formulation, a parametric study was conducted on the effects of sag-extensibility and bending stiffness. The formulation is verified with available theoretical solutions and compared with finite-element analyses. Capabilities of this formulation are demonstrated through examples. A simple relationship among nondimensional cable parameters is also introduced for the range of parameters applicable to stay cables in cable-stayed bridges. This simple relationship provides an accurate tool for measurement of tension forces in stay cables using the vibration method.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Casas, J. R.(1994). “A combined method for measuring cable forces: the cable-stayed Alamillo Bridge, Spain.”Struct. Engrg. Int., 3, 235–240.
2.
Crandall, S. H., and McCalley Jr., R. B. (1996). “Chapter 28: matrix methods of analysis.”Handbook of shock and vibration, M. H. Harris, ed., McGraw-Hill, New York. EISPACK: A package for solving matrix eigenvalue problems. (1997). Mathematics and Comp. Sci. Div., Argonne National Laboratory, Argonne, Ill.
3.
Irvine, M. (1992). Cable structures. Dover Publications, Inc., New York. NISA II: numerically integrated elements for system analysis. (1995). Engineering Mechanics Research Corporation, Troy, Mich.
4.
Robert, J. L., Bruhat, D., Gervais, J. P., and Chatelain, J. (1991). “Mesure de la tension des cables par methode vibratoire.”Bulletin de liaison des laboratoires des ponts et Chaussees, France, 173, 109–114 (in French).
5.
Starossek, U.(1991). “Dynamic stiffness matrix of sagging cable.”J. Struct. Engrg., ASCE, 117(12), 2815–2829.
6.
Starossek, U.(1994). “Cable dynamics—a review.”Struct. Engrg. Int., 3, 171–176.
7.
Tabatabai, H., Mehrabi, A. B., Morgan, B. J., and Lotfi, H. R. (1997). “Nondestructive bridge evaluation technology: bridge stay cable condition assessment.”Report to the Federal Highway Administration, Construction Technology Laboratories, Inc., Skokie, Ill.
8.
Zui, H., Shinke, T., and Namita, Y.(1996). “Practical formulas for estimation of cable tension by vibration method.”J. Struct. Engrg., ASCE, 122(6), 651–656.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 124 • Issue 11 • November 1998
Pages: 1313 - 1322
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Nov 1, 1998
Published in print: Nov 1998
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.