Abstract
This paper investigates the dynamic behavior of a cable considering geometrical nonlinearity due to the sagging effect, based on the elastic catenary cable thoery. The finite element method has been limited in application to the dynamic analysis of a cable element because its displacement interpolation function can not be obtained from the boundary conditions. This paper proposes a derivation of the interpolation function for spatially suspended catenary cable, using the flexibility matrix. Equations for the compatibility conditions of a catenary cable are derived under mutiple concentrated loads within an element. Also, self-weight and other vairous types of distributed load imposed within an element are discritized with equivalent concentrated loads at multiple Gaussian points. Dynamic inertia and damping forces along the cable profile are assumed to be distributed according to the developed interpolation functions so that internal forces are evaluated directly from the compatibility equations and flexiblity matrix. The proposed element is verified through an experiment testing the free vibration of a suspension cable, and the dynamic bahevior of a suspension cable is compared with the ABAQUS beam element where three-dimensional support excitations are imposed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ann, S. S. (1991). Static and Dynamic Nonlinear Analysis of Spatial Cable Networks using Elastic Catenary cable Element, Master thesis, Seoul National University, Seoul, Korea.
Chang, S. P. and Park, J. I. (1989). “A study on the Nonlinear Finite Cable Element.” Journal of Korean Society of Coastal and Ocean Engineers, Vol. 1, No. 1, pp. 93–101.
Irivine, H. M. (1981). Cable Structures, MIT press.
Kim, J. and Chang, S. P. (2001). “Dynamic stiffness matrix of an inclined cable.” Engineering Structures, Vol. 23, pp. 1614–1621.
Koh, H. M. (2007). Estimation of the Modal Damping Ratio in Stay Cable by Free Vibration and Forced Vibration Test, Korea Bridge Design and Engineering Research Center, Seoul, Korea.
Lee, D. I. (1990). The Static Analysis of the Cable Member by FEM, Master thesis, Seoul National University, Seoul, Korea.
Leonard, J. W and Recker, W. W (1972). “Nonlinear dynamics of cables with low initial tension.” Jounral of Engineering Mechacnics, ASCE., Vol. 98, pp.293–309.
Mesarovic, S. and Gasparini, D. A (1992b). “Dynamic bahavior of nonlinear cable system. II.” Journal of Engineering Mechanics, ASCE, Vol. 118, No. 5, pp. 904–920.
Park, Y. Y. (1992). Dynamic Analysis of Cable-Suspended Roof System Subjected to a Wind Load, PhD thesis, Seoul National University, Seoul, Korea.
Park, J. I. (1993). Dynamic Analysis of Tension Leg Platform Using 3D-Curved Surface Boundary Element Methods, PhD thesis, Seoul National University, Seoul, Korea.
Veletsos, A. S. and Darbre, G. R. (1983). “Free Vibration of Parabolic Cables.” Journal of Sturctural Engineering, ASCE, Vol. 109, No. 2, pp. 503–519.
Volokh, K. Y., Vilnay, O., Averbuh, I. (2003). “Dynamics of Cable Structures.” Journal of Sturctural Engineering, ASCE, Vol. 129, No. 2, pp. 175–180.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, SP., Park, JI. & Lee, KC. Nonlinear dynamic analysis of spatially suspended elastic catenary cable with finite element method. KSCE J Civ Eng 12, 121–128 (2008). https://doi.org/10.1007/s12205-008-0121-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-008-0121-1