Abstract
The nonlinear interaction of the first two in-plane modes of a suspended cable with a moving fluid along the plane of the cable is studied. The governing equations of motion for two-mode interaction are derived on the basis of a general continuum model. The interaction causes the modal differential equations of the cable to be non-self-adjoint. As the flow speed increases above a certain critical value, the cable experiences oscillatory motion similar to the flutter of aeroelastic structures. A co-ordinate transformation in terms of the transverse and stretching motions of the cable is introduced to reduce the two nonlinearly coupled differential equations into a linear ordinary differential equation governing the stretching motion, and a strongly nonlinear differential equation for the transverse motion. For small values of the gravity-to-stiffness ratio the dynamics of the cable is examined using a two-time-scale approach. Numerical integration of the modal equations shows that the cable experiences stretching oscillations only when the flow speed exceeds a certain level. Above this level both stretching and transverse motions take place. The influences of system parameters such as gravity-to-stiffness ratio and density ratio on the response characteristics are also reported.
Similar content being viewed by others
References
Irvine, M. and Caughey, T. K., ‘The linear theory of free vibrations of a suspended cable’, Proceedings of the Royal Society of London, Series A 341, 1974, 299–315.
Irvine, M., Cable Structures, Dover, New York, 1992.
Luongo, A., Rega, G., and Vestroni, F., ‘Planar nonlinear vibrations of an elastic cable’, International Journal of Non-Linear Mechanics 19(1), 1984, 39–52.
Takahashi, K. and Konishi, Y., ‘Nonlinear vibrations of cables in three dimensions, Part i: Non-linear free vibrations’, Journal of Sound and Vibration 118(1), 1987, 69–84.
Casarella, M. J. and Parsons, M., ‘Cable systems under hydrodynamic loading’, Marine Technology Society Journal 4, 1970, 27–44.
Choo, Y. and Casarella, M. J., ‘A survey of analytical methods for dynamic simulation of cable-body systems’, Journal of Hydronautics 7, 1973, 137–144.
Williams, H. E., ‘Motion of a cable used as a mooring’, Journal of Hydronautics 9(7), 1975, 107–118.
Goodman, T. R. and Breslin, J. P., ‘Statics and dynamics of anchoring cables in waves’, Journal of Hydronautics 10(4), 1976, 113–142.
Demler, T. N. and Stephens, T. C., ‘Numerical simulation of towed cables’, Ocean Engineering 10(2), 1983, 119–132.
Ablow, C. M. and Schechter, S., ‘Numerical simulation of undersea cable dynamics’, Ocean Engineering 10(6), 1983, 443–457.
Milinazzo, F., Wilkie, M., and Latchman, S. A., ‘An efficient algorithm for simulating the dynamics of towed cable systems’, Ocean Engineering 14(6), 1987, 513–526.
Delmer, T. N., Stephens, T. C., and Tremills, J. A., ‘Numerical simulation of cable-towed acoustic arrays’, Ocean Engineering 15(6), 1988, 511–548.
Papazoglou, V. J., Mavrokos, S. A., and Triantafyllou, M. S., ‘Nonlinear cable response and model testing in water’, Journal of Sound and Vibration 140(1), 1990, 103–115.
Hover, F. S., Grosenbaugh, M. A., and Triantafyllou, M. S., ‘Calculation of dynamic motions and tensions in towed underwater cables’, IEEE Journal of Oceanic Engineering 19(3), 1994, 449–457.
Calkins, D. E., ‘Faired towline hydrodynamics’, Journal of Hydronautics 4, 1970, 113–119.
Cannon, T. C. and Genin, J., ‘Dynamic behavior of material damped flexible towed cable’, Aeronautical Quarterly 23, 1972, 109–120.
Nair, S. and Hegemier, G., ‘Stability of faired underwater towing cables’, Journal of Hydronautics 13, 1979, 20–27.
Hung, C. Y. and Nair, S., ‘Planar towing and hydroelastic stability of faired underwater cables’, AIAA Journal 22(12), 1984, 1786–1790.
Pilipchuk, V. N., ‘Method of investigating nonlinear dynamics problems of rectangular plates with initial imperfections’, Soviet Applied Mechanics 22(2), 1986, 162–168.
Blevins, R. D., Flow-Induced Vibration, Van Nostrand Reinhold, New York, 1977.
Morison, D., O'Brien, M., Johnson, J., and Schaaf, S., ‘The force excerted by surface waves on piles’, Petroleum Transactions AIME 189, 1950, 149–154.
Nayfeh, A. H., Perturbation Methods, Wiley, New York, 1973, pp. 240–241.
Kevorkian, J. and Cole, J. D., Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981, pp. 115–119.
Chang, W. K., ‘Nonlinear mixed mode dynamics of suspended cables under random excitation and fluid flow interaction’, Ph.D. Dissertation, Wayne State University, Detroit, MI, 1997.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chang, W.K., Pilipchuk, V. & Ibrahim, R.A. Fluid Flow-Induced Nonlinear Vibration of Suspended Cables. Nonlinear Dynamics 14, 377–406 (1997). https://doi.org/10.1023/A:1008223909270
Issue Date:
DOI: https://doi.org/10.1023/A:1008223909270