Abstract
The nonlinear oscillations of a controlled suspended elastic cable under in-plane excitation are considered. Active control realized by longitudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadratic enhanced velocity feedback control laws are chosen and their effects on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane steady-state solutions and their stability under an out-of-plane disturbance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence of the control effectiveness on the system parameters is investigated in the case of the first symmetric mode and the range of oscillation amplitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quantities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered when the motion is characterized by two comparable components.
Similar content being viewed by others
References
Nayfeh, A. H. and Balachadran, B., ‘Modal interactions in dynamical and structural systems’, Applied Mechanics Review 42, 1989, S175–S202.
Benedettini, F. and Rega, G., ‘Non-linear dynamics of an elastic cable under planar excitation’, International Journal of Non-Linear Mechanics 22, 1987, 497–509.
Takahashi, K. and Konishi, Y., ‘Non-linear vibrations of cables in three dimensions, Part I: Non-linear free vibrations; Part II: Out-of-plane vibration under in-plane sinusoidally time varying load’, Journal of Sound and Vibration 118, 1987, 69–97.
Benedettini, F., Rega, G., and Alaggio R., ‘Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonant conditions’, Journal of Sound and Vibration 185, 1995, 775–798.
Perkins, N. C., ‘Modal interactions in the non-linear response of elastic cables under parametric/external excitation’, International Journal of Non-Linear Mechanics 27, 1992, 233–250.
Lee, C. L. and Perkins, N. C., ‘Nonlinear oscillations of suspended cables containing a two-to-one internal resonance’, Nonlinear Dynamics 3, 1992, 465490.
Pacheco, B. M., Fujino, Y., and Sulekh, A., ‘Estimation curve for modal damping in stay cables with viscous damper’, Journal of Structural Engineering, ASCE 119, 1993, 1961–1979.
Hagedorn, P., ‘Active vibration damping in large flexible structures’, in Proceedings of the 17th International Congress of Theoretical and Applied Mechanics, Grenoble, France, 1988, pp. 83–100.
Yamaguchi, H. and Dung, N. N., ‘Active wave control of sagged-cable vibration’, in Proceedings 1st International Conference on Motion and Vibration Control, JSME, 1992, pp. 134–139.
Chen, J. C., ‘Response of large space structures with stiffness control’, Journal of Spacecraft and Rockets 21, 1984, 463–467.
Fujino, Y., Warnitchai, P., and Pacheco, B.M., ‘Active stiffness control of cable vibration’, Journal of Applied Mechanics 60, 1993, 984–953.
He, X. and Powell, J. D., ‘Tether damping in space’, Journal of Guidance, Dynamics and Control 13, 1990, 104–112.
Fujino, Y. and Susumpow, T., ‘An experimental study on active control of in-plane cable vibrations by axial support motion’, Earthquake Engineering and Structural Dynamics 23, 1994, 1283–1297.
Vestroni, F., Pasca, M., and Gattulli, V., ‘Controlled nonlinear motions of a suspended cable’, in Proceedings of International Symposium on Cable Dynamics, Liege, Belgium, October 19–21, 1995, pp. 413–420.
Pasca, M., Gattulli, V., and Vestroni, F., ‘Active control of spatial cable oscillations’, in Structural Dynamics – EURODYN'96, G. Augusti, C. Borri, and P. Spinelli (eds.), Balkema, Rotterdam, 1996, pp. 591–598.
Luongo, A., Rega, G., and Vestroni, F., ‘Planar non-linear free vibrations of an elastic cable’, International Journal of Non-Linear Mechanics 19, 1984, 39–52.
Irvine, H. M. and Caughey, T. K., ‘The linear theory of free vibrations of suspended cable’, Proceedings of the Royal Society of London, Series A 341, 1974, 299–315.
Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.
Luongo, A., Rega, G., and Vestroni, F., ‘On nonlinear dynamics of planar shear indeformable beams’, Journal of Applied Mechanics 53, 1986, 619–624.
Nayfeh, A. H. and Sanchez, N. E., ‘Bifurcations in a forced softening duffing oscillator’, International Journal of Non-Linear Mechanics 24, 1989, 483–497.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gattulli, V., Pasca, M. & Vestroni, F. Nonlinear Oscillations of a Nonresonant Cable under In-Plane Excitation with a Longitudinal Control. Nonlinear Dynamics 14, 139–156 (1997). https://doi.org/10.1023/A:1008255409438
Issue Date:
DOI: https://doi.org/10.1023/A:1008255409438