Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Hybrid nonlinear control of a tall tower with a pendulum absorber

  • Orlando, Diego (Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro) ;
  • Goncalves, Paulo B. (Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro)
  • Received : 2012.07.05
  • Accepted : 2013.03.29
  • Published : 2013.04.25
⟨ Previous Next ⟩

Abstract

Pendulums can be used as passive vibration control devices in several structures and machines. In the present work, the nonlinear behavior of a pendulum-tower system is studied. The tower is modeled as a bar with variable cross-section with concentrated masses. First, the vibration modes and frequencies of the tower are obtained analytically. The primary structure and absorber together constitute a coupled system which is discretized as a two degrees of freedom nonlinear system, using the normalized eigenfunctions and the Rayleigh-Ritz method. The analysis shows the influence of the geometric nonlinearity of the pendulum absorber on the response of the tower. A parametric analysis also shows that, with an appropriate choice of the absorber parameters, a pendulum can decrease the vibration amplitudes of the tower in the main resonance region. The results also show that the pendulum nonlinearity cannot be neglected in this type of problem, leading to multiplicity of solutions, dynamic jumps and instability. In order to improve the effectiveness of the control during the transient response, a hybrid control system is suggested. The added control force is implemented as a non-linear variable stiffness device based on position and velocity feedback. The obtained results show that this strategy of nonlinear control is attractive, has a good potential and can be used to minimize the response of slender structures under various types of excitation.

Keywords

References

  1. Azadi, M., Behzadipour, S. and Faulkner, G. (2009), "Antagonistic variable stiffness elements", Mechanism and Machine Theory, 44(9), 1746-1758. https://doi.org/10.1016/j.mechmachtheory.2009.03.002
  2. Azadi, M., Behzadipour, S. and Faulkner, G. (2011), "Performance analysis of a semi-active mount made by a new variable stiffness spring", Journal of Sound and Vibration, 330(12), 2733-2746. https://doi.org/10.1016/j.jsv.2011.01.010
  3. Battista, R.C., Rodrigues, R.S. and Pfeil, M.S. (2003), "Dynamic behavior and stability of transmission line towers under wind forces", Journal of Wind Engineering and Industrial Aerodynamics, 91(8), 1051-1067. https://doi.org/10.1016/S0167-6105(03)00052-7
  4. Cicek, I. (2002), "Experimental investigation of beam-tip mass and pendulum system under random excitation", Mechanical Systems and Signal Processing, 16(6), 1059-1072. https://doi.org/10.1006/mssp.2001.1475
  5. Clark, W.W. (2000), "Vibration control with state-switched piezoelectric materials", Journal of Intelligent Material Systems and Structures, 11(4), 263-271. https://doi.org/10.1106/18CE-77K4-DYMG-RKBB
  6. Collette, F.S. (1998), "A combined tuned absorber and pendulum impact damper under random excitation", Journal of Sound and Vibration, 216(2), 199-213. https://doi.org/10.1006/jsvi.1997.1666
  7. Den Hartog, J. P. (1985), Mechanical Vibrations, Dover Publications, NY.
  8. Ertas, A., Cuvalci, O. and Ekwaro-Osire, S. (2000), "Performance of pendulum absorber for a nonlinear system of varying orientation", Journal of Sound and Vibration, 229(4), 913-933. https://doi.org/10.1006/jsvi.1999.2521
  9. Fischer, O. (2007), "Wind-excited vibrations-solution by passive dynamic vibration absorbers of different types", Journal of Wind Engineering and Industrial Aerodynamics, 95, 1028-1039. https://doi.org/10.1016/j.jweia.2007.01.027
  10. Gerges, R.R. and Vickery, B.J. (2003), "Parametric experimental study of wire rope spring tuned mass dampers", Journal of Wind Engineering and Industrial Aerodynamics, 91, 1363-1385. https://doi.org/10.1016/j.jweia.2003.09.038
  11. Goncalves, P.B. and Orlando, D. (2007), "Influence of a pendulum absorber on the nonlinear behavior and instabilities of a tall tower", IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty 2007, Eds. H.Y. Hu and E. Kreuzer, Springer, The Netherlands.
  12. Gonçalves, P.B. and Santee, D. (2008), "Influence of uncertainties on the dynamic buckling loads of structures liable to asymmetric post-buckling behavior", Mathematical Problems in Engineering, doi:10.1155/2008/490137.
  13. Goncalves, P.B., Silva, F.M.A., Rega, G. and Lenci, S. (2011), "Global dynamics and integrity of a two-dof model of a parametrically excited cylindrical shell," Nonlinear Dynamics, 63, 61-82. https://doi.org/10.1007/s11071-010-9785-4
  14. Hassani, F.A., Payam A.F. and Fathipour, M. (2010), "Design of a smart MEMS accelerometer using nonlinear control principles", Smart Structures and Systems 6, 1-16 https://doi.org/10.12989/sss.2010.6.1.001
  15. Korenev, B.G. and Reznikov, L.M. (1993), Dynamic Vibration Absorbers: Theory and Technical Aplications, John Wiley & Sons, Chichester.
  16. Kourakis, I. (2007), "Structural systems and tuned mass dampers of super-tall buildings: case study of Taipei 101", Maters Thesis, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology.
  17. Leitmann, G. (1994), "Semiactive control for vibration attenuation", Journal of Intelligent Material Systems and Structures, 5, 841-846. https://doi.org/10.1177/1045389X9400500616
  18. Li, Q.S., Shang, G.Q., Huang, S.H. and Tuan, A.Y. (2011), "Wind-Induced Vibration Control of a Super- Tall Building with TMD", Proceedings of the 13th International Conference on Wind Enginnering, Amsterdam.
  19. Liu, K., Chen, L.X., and Cai, G.P. (2011), "Active control of a nonlinear and hysteretic building structure with time delay", Structural Engineering and Mechanics, 40(3), 431-451. https://doi.org/10.12989/sem.2011.40.3.431
  20. Macias-Cundapi, L., Silva-Navarro, G. and Vázquez-Gonzalez, B. (2008), "Application of an Active Pendulum-Type Vibration Absorber for Duffing Systems", Proceedings of the 5th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE 2008) IEEE Catalog Number: CFP08827-CDR, ISBN: 978-1-4244-2499-3.
  21. Matta, E. and De Stefano, A. (2009), "Robust design of mass-uncertain rolling-pendulum TMDs for the seismic protection of buildings", Mechanical Systems and Signal Processing, 23, 127-147. https://doi.org/10.1016/j.ymssp.2007.08.012
  22. Mustafa, G. and Ertas, A. (1995), "Dynamics and Bifurcations of a Coupled Column-Pendulum Oscillator", Journal of Sound and Vibration, 182(3), 393-413. https://doi.org/10.1006/jsvi.1995.0207
  23. Nagarajaiah, S. and Varadarajan, N. (2005), "Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD", Engineering Structures, 27, 431-441. https://doi.org/10.1016/j.engstruct.2004.10.015
  24. Nagase, T. and Hisatoku, T. (1992), "Tuned-pendulum mass damper installed in crystal tower", The Structural Design of Tall Buildings, 1, 35-56. https://doi.org/10.1002/tal.4320010105
  25. Naprstek, J. and Fischer, C. (2009), "Auto-parametric semi-trivial and post-critical response of a spherical pendulum damper", Computers and Structures, 87, 1204-1215. https://doi.org/10.1016/j.compstruc.2008.11.015
  26. Nitzsche, F., Grewal, A. and Zimcik, D.G. (1999), "Structural component having means for actively varying its stiffness to control vibrations", US patent 5, 973, 440.
  27. Nitzsche, F., Zimcik, D.G., Wickramashinghe, V. and Chen, Y. (2004), "Control laws for an active tunable vibration absorber designed for rotor blade damping augmentation", Aeronautical Journal, 108(1), 35-42. https://doi.org/10.1017/S0001924000004978
  28. Orlando, D. (2006), "Pendulum Absorber for Vibration Control of Tall Towers", M.Sc. Dissertation, DEC - PUC-Rio, Rio de Janeiro, Brazil. (in Portuguese)
  29. Oueini, S.S., Nayfeh, H. and Pratt, J.R. (1999), "The Review of Development and Implementation of Active Non-Linear Vibration Absorber", Archive of Applied Mechanics, 69, 585-620. https://doi.org/10.1007/s004190050245
  30. Pnevmatikos, N.K., Kallivokas, L.K., Gantes, C.J. (2004), "Feed-forward control of active variable stiffness systems for mitigating seismic hazard in structures", Engineering Structures 26, 471-483. https://doi.org/10.1016/j.engstruct.2003.11.003
  31. Pirner, M. (2002), "Actual behaviour of a ball vibration absorber", Journal of Wind Engineering and Industrial Aerodynamics, 90, 987-1005. https://doi.org/10.1016/S0167-6105(02)00215-5
  32. Qiusheng, L., Hong, C. and Guiqing, L. (1994), "Static and dynamic analysis of straight bars with variable cross-section", Computers and Structures, 59, 1185-1191.
  33. Ramaratnam, A. and Jalili, N. (2006), "A switched stiffness approach for structural vibration control: theory and real-time implementation", Journal of Sound and Vibration, 291, 258-274. https://doi.org/10.1016/j.jsv.2005.06.012
  34. Ramaratnam, A., Jalili, N. and Dawson, D.M. (2004), "Semi-active vibration control using piezoelectricbased switched stiffness", Proceedings of American Control Conference, Boston, MA.
  35. Rega, G. and Lenci, S. (2005), "Identifying, evaluating and controlling dynamical integrity measures in nonlinear mechanical oscillators", Nonlinear Analysis, 63, 902-914. https://doi.org/10.1016/j.na.2005.01.084
  36. Rodríguez, A.G., Chacón, J.M., Donoso, A. and Rodríguez, A.G.G. (2011), "Design of an adjustablestiffness spring: Mathematical modeling and simulation, fabrication and experimental validation", Mechanism and Machine Theory, 46, 1970-1979. https://doi.org/10.1016/j.mechmachtheory.2011.07.002
  37. Spencer, B. and Nagarajaiah, S. (2003), "State of the art of structural control", J. Struct. Eng., 129(7), 845- 856. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845)
  38. Soliman, M.S. (1994), "Global transient dynamics of nonlinear parametrically excited systems", Nonlinear Dynamics, 6(3), 317-329. https://doi.org/10.1007/BF00053389
  39. Soliman, M.S. and Goncalves, P.B. (2003), "Chaotic behavior resulting in transient and steady state instabilities of pressure-loaded shallow spherical shells", Journal of Sound and Vibration, 259, 497-512. https://doi.org/10.1006/jsvi.2002.5163
  40. Soliman, M.S. and Thompson, J.M.T. (1989), "Integrity measures quantifying the erosion of smooth and fractal basins of attraction", Journal of Sound Vibration, 135, 453-475. https://doi.org/10.1016/0022-460X(89)90699-8
  41. Sonneborn, L. and Van Vleck, F. (1965), "The bang-bang principle for linear control systems", SIAM J. Control, 2, 151-159.
  42. Soong, Y.T. (1988), "State-of-the-art review: active control in civil engineering", Eng. Struct., 10, 74-83. https://doi.org/10.1016/0141-0296(88)90033-8
  43. Soong, T.T. and Dargush, G.F. (1997), Energy Dissipation Systems in Structural Engineering, John Wiley & Sons, Chichester.
  44. Tang, D., Gavin, H.P. and Dowell, E.H. (2004), "Study of airfoil gust response alleviation using an electromagnetic dry friction damper - part 1: theory", Journal of Sound and Vibration, 269(20), 853-874. https://doi.org/10.1016/S0022-460X(03)00180-9
  45. Thompson, J.M.T. (1989), "Chaotic behavior triggering the escape from a potential well", Proc. Roy. Soc. London A, 421, 195-225. https://doi.org/10.1098/rspa.1989.0009
  46. Vyas, A. and Bajaj, A.K. (2001), "Dynamics of autoparametric vibration absorbers using multiple pendulums", Journal of Sound and Vibration, 246(1), 115-135. https://doi.org/10.1006/jsvi.2001.3616
  47. Warminski, J. and Kecik, K. (2009), "Instabilities in the main parametric resonance area of a mechanical system with a pendulum", Journal of Sound and Vibration, 322, 612-628. https://doi.org/10.1016/j.jsv.2008.06.042
  48. Warminski, J. and Kecik, K. (2012), "Autoparametric vibrations of a nonlinear system with a pendulum and magnetorheological damping", Nonlinear Dynamic Phenomena in Mechanics Solid Mechanics and Its Applications, 181, 1-61 https://doi.org/10.1007/978-94-007-2473-0_1
  49. Winthrop, M.F., Baker, W.P. and Cobb, R.G. (2005), "A variable stiffness device selection and design tool for lightly damped structures", Journal of Sound and Vibration, 287, 667-682. https://doi.org/10.1016/j.jsv.2004.11.022
  50. Wu, B., Liu, F.T. and Wei, D.M. (2005), "Approximate analysis method for interstorey shear forces in structures with active variable stiffness systems", Journal of Sound and Vibration, 286, 963-980. https://doi.org/10.1016/j.jsv.2004.10.032
  51. Wu, S.T. (2009), "Active pendulum vibration absorbers with a spinning support", Journal of Sound and Vibration, 323, 1-16. https://doi.org/10.1016/j.jsv.2008.12.017
  52. Wu, S.T., Chen, Y.R. and Wang, S.S. (2011), "Two-degree-of-freedom rotational-pendulum vibration absorbers", Journal of Sound and Vibration, 330, 1052-1064. https://doi.org/10.1016/j.jsv.2010.09.028
  53. Yaman, M. and Sen, S. (2004), "The analysis of the orientation effect of non-linear flexible systems on performance of the pendulum absorber", International Journal of Non-Linear Mechanics, 39, 741-752. https://doi.org/10.1016/S0020-7462(03)00038-6

Cited by

  1. Damping optimization over the arbitrary time of the excited mechanical system vol.304, 2016, https://doi.org/10.1016/j.cam.2016.03.005
  2. Realization of Artificial Nonlinear Spring with Controllable Stiffness vol.09, pp.08, 2017, https://doi.org/10.1142/S1758825117501198
  3. Modified pendular vibration absorber for structures under base excitation vol.66, pp.2, 2013, https://doi.org/10.12989/sem.2018.66.2.161
  4. Optimal Pendulum Tuned Mass Damper Design Applied to High Towers Using Genetic Algorithms: Two-DOF Modeling vol.19, pp.10, 2013, https://doi.org/10.1142/s0219455419501256
  5. Effectiveness of tuned mass damper system for steel frame building vol.869, pp.None, 2013, https://doi.org/10.1088/1757-899x/869/5/052075
  6. Exploration of the Nonlinear Effect of Pendulum Tuned Mass Dampers on Vibration Control vol.147, pp.8, 2021, https://doi.org/10.1061/(asce)em.1943-7889.0001961