DOI QR코드

DOI QR Code

Active feedback control for cable vibrations

  • Received : 2006.12.13
  • Accepted : 2008.11.15
  • Published : 2008.07.25

Abstract

The nonlinear mechanics of cable vibration is caught either by analytical or numerical models. Nevertheless, the choice of the most appropriate method, in consideration of the problem under study, is not straightforward. A feedback control policy might even enhance the complexity of the system. Thus, in order to design a suitable controller, different approaches are here adopted. Devices mounted transversely to the cable in the two directions, close to one of its ends, supply the feedback control action based on the observation of the response in a few points. The low order terms of the control law are, at first, analyzed in the framework of linear models. Explicit analytic solutions are derived for this purpose. The effectiveness of high order terms in the control law is then explored by means of a finite element model(FEM), which accounts for high order harmonics. A suitably dimensional analytical Galerkin model is finally derived, to investigate the effectiveness of the proposed control strategy, when applied to a physical model.

Keywords

References

  1. Abdel-Rohman, M. and Spencer, B. F. (2004), "Control of wind-induced nonlinear oscillations in suspended cables", Nonlin. Dyn., 37, 341-355. https://doi.org/10.1023/B:NODY.0000045545.87106.cc
  2. Alaggio, R., Gattulli, V. and Potenza, F. (2006). "Experimental validation of longitudinal active control strategy for cable oscillations", Proceedings of the 9 th INVENTO Italian Conference on Wind Engineering, Pescara, June.
  3. Arafat, H. N. and Nayfeh, A. H. (2003), "Nonlinear responses of suspended cables to primary resonance excitations", J. Sound Vib., 266, 325-354. https://doi.org/10.1016/S0022-460X(02)01393-7
  4. Benedettini, F., Rega, G. and Alaggio, R. (1995), "Nonlinear oscillations of four-degree of freedom model of a suspended cable under multiple internal resonance conditions", J. Sound Vib., 182, 775-798. https://doi.org/10.1006/jsvi.1995.0232
  5. Cai, C. S., Wu, W. J. and Shi, X. M. (2006), "Cable vibration reduction with a hung-on TMD system. Part I: Theoretical study", J. Vib. Control, 12(7), 801-814. https://doi.org/10.1177/1077546306065857
  6. Cai, C. S., Wu, W. J. and Shi, X. M. (2006), "Cable vibration reduction with a hung-on TMD system. Part II: Parametric study", J. Vib. Control, 12(8), 881-899. https://doi.org/10.1177/1077546306065858
  7. Casciati, F., Magonette, G. and Marazzi, F. (2006), Technology of Semiactive Devices and Applications in Vibration Mitigation, John Wiley & Sons, Chichester.
  8. Casciati, F., and Ubertini, F. and Marazzi, F. (2007), "Nonlinear vibration of shallow cables with semi-active tuned mass damper", Nonlin. Dyn., in press, DOI 10.1007/s11007-007-9298-y.
  9. Casciati, F., Fuggini, C. and Bonanno C. (2007), "Dual frequency GPS receivers: reliability of precision of the measures", Proceedings of 4 colloque Interdisciplinaire en Instrumentation, Nancy, October.
  10. Cluni, F., Gusella, V. and Ubertini, F. (2007), "A parametric investigation of wind-induced cable fatigue", Eng. Struct., 29(11), 3094-3105. https://doi.org/10.1016/j.engstruct.2007.02.010
  11. Doedel, E. J., Paffenroth, R. C., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Oldeman, B. E., Sandstede, B. and Wang, X., AUTO 2000: Continuation and bifurcation software for ordinary differential equations, available online from http://indy.cs.concordia.ca/auto/.
  12. Faravelli, L. and Ubertini, F. (2007), "Observability issues in the vibration of cables", Proceedings of COMPDYN 2007 ECCOMAS Thematic Conference, Crete, June.
  13. Gattulli, V., Pasca, M. and Vestroni, F. (1997), "Nonlinear oscillations of nonresonant cable under in-plane excitation with a longitudinal control", Nonlin, Dyn., 14(2), 139-156. https://doi.org/10.1023/A:1008255409438
  14. Gattulli, V., and Vestroni, F. (2000), "Nonlinear strategies for longitudinal control in the stabilization of an oscillating suspended cable", Dyn. Control, 10(4), 359-374. https://doi.org/10.1023/A:1011273600500
  15. Gattulli, V., Martinelli, L., Perotti, F. and Vestroni, F. (2004), "Nonlinear oscillations of cables under harmonic loading using analytical and finite element models", Comput. Meth. Appl. Mech. Eng., 193, 69-85. https://doi.org/10.1016/j.cma.2003.09.008
  16. Hilber, H. M., Hughes, T. J. R. and Taylor, R. L. (1997), "Improved numerical dissipation for time integration algorithms in structural dynamics", Earthq. Eng. Struct. Dyn., 5, 283-292.
  17. Hui Li, Min, Liu and Jinping, Ou (2004), "Vibration mitigation of a stay cable with one shape memory alloy damper", Structural Control Health Monit., 11, 21-36. https://doi.org/10.1002/stc.29
  18. Irvine, H. M. and Caughey, T. K. (1974), "The linear theory of free vibrations of suspended cables", Proceedings of the Royal Society of London 341, 299-315. https://doi.org/10.1098/rspa.1974.0189
  19. Johnson, E. A., Christenson, RE. and Spencer, Jr., B. F. (2001), "Smart stay cable damping effects of sag and inclination", Proceeding of '01 ICOSSAR, Newport Beach, June.
  20. Kolovsky, M. Z. (1996), Nonlinear Dynamics of Active and Passive Systems of Vibration Protection, Springer Verlag, Berlin.
  21. Larsen, J. W. and Nielsen, S. R. K. (2004), "Non-linear stochastic response of a shallow cable", Int. J. Non Lin. Mech., 41, 327-344.
  22. Luongo, A., Rega, G. and Vestroni, F. (1984), "Parametric analysis of Large amplitude free vibrations of a suspended cable", Int. J. Solids Struct., 20, 95-105. https://doi.org/10.1016/0020-7683(84)90001-5
  23. Nayfeh, A. H., Arafat, H. N., Chin, C. M. and Lacarbonara, W. (2002), "Multimode interactions in suspended cables", J. Vib. Control, 8, 337-387. https://doi.org/10.1177/107754602023687
  24. Pacheko, B. M., Fujino, Y. and Sulekh, A. (1990), "Estimation curve for modal damping in stay cables with viscous dampers", ASCE J. Struct. Eng., 119(6), 1961-1979.
  25. Pasca, M., Vestroni, F. and Gattulli, V. (1998), "Active longitudinal control of wind-induced oscillations of a suspended cable", Meccanica 33, 255-266. https://doi.org/10.1023/A:1004347130512
  26. Rega, G. (2004), "Nonlinear vibrations of suspended cables - Part I: modeling and analysis", Appl. Mech. Rev., 57, 443-478. https://doi.org/10.1115/1.1777224
  27. Rega, G. (2004), "Nonlinear vibrations of suspended cables - Part 2: deterministic phenomena", Appl. Mech. Rev., 57, 479-514. https://doi.org/10.1115/1.1777225
  28. Soong, T. T. and Dargush G. F. (1997), Passive Evergy Dissipation Systems in Structural Engineering, John Wiley & Sons, Chichester.
  29. Srinil, N. and Rega, G. (2007), "Two-to-one resonant multi modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation", Nonlin. Dyn., 48(3), 231-252. https://doi.org/10.1007/s11071-006-9086-0
  30. Srinil, N. and Rega, G. (2007), "Two-to-one resonant multi modal dynamics of horizontal/inclined cables Part II: Internal resonance activation, reduced order models and nonlinear normal modes", Nonlin. Dyn., 48(3), 253- 274. https://doi.org/10.1007/s11071-006-9087-z
  31. Staszewski, W. J. (1997), "Identification of damping in mdof systems using time-scale decomposition", J. Sound Vib., 203(2), 283-305. https://doi.org/10.1006/jsvi.1996.0864
  32. Susumpow, T. and Fujino, Y. (1995), "Active control of multimodal cable vibrations by axial support motion", Earthq. Eng. Struct. Dyn., 5, 283-292.
  33. The mathworks Inc (2002), Matlab and Simulink Natick MA.
  34. Ubertini, F. and Domaneschi, M. (2006), "Analytic and numeric approach to controlled cables", Proceedings of the 16th Italian Conference on Computational Mechanics Bologna, June.
  35. Ubertini, F. and Fuggini, C. (2007), "Confronto di due tecniche sperimentali per l'identificazione e il monitoraggio dei cavi strutturali" (in Italian), Proceedings of AIPND conference, Milano, October.
  36. Xu, Y. L. and Yu, Z. (1999), "Non-linear vibration of cable damper system. Part I: formulartion", J. Sound Vib. 225, 447-463. https://doi.org/10.1006/jsvi.1999.2203
  37. Xu, Y. L. and Yu, Z, (1999) "Non-linear vibration of cable damper system. Part II: application and verification", J. Sound Vib. 225, 465-481. https://doi.org/10.1006/jsvi.1999.2204
  38. Wu, W. J. and Cai, C. S. (2006), "Experimental study of magnetorheological dampers and application to cable vibration control", J. Vib. Control, 12(1), 67-82. https://doi.org/10.1177/1077546306061128
  39. Zhou, Q. Nielsen, S. R. K. and Qu, W. L. (2006), "Semi active control of three dimensional vibrations of an inclined sag cable with magnetorheological dampers", J. Sound Vib., 296, 1-22. https://doi.org/10.1016/j.jsv.2005.10.028

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