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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu


Bistability and Bursting Oscillations in Electromechanical Butterfly Valves

Journal of Applied Nonlinear Dynamics 2(3) (2013) 303--314 | DOI:10.5890/JAND.2013.08.005

C.A. Kitio Kwuimy; C. Nataraj

Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USA

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Abstract

This papers considers an electromechanical butterfly valve and discusses the conditions for appearance of bistability and bursting oscillations. The critical nonlinear stiffness coefficient and inlet velocities leading to such dynamics are obtained as a function of the system parameters, and the effects of external perturbation on the bursting response of the system are illustrated. It is observed that the driving parameters and the direct current voltage strongly affect the sharpness, the number of strikes, the amplitude of the strikes and the time interval between the strikes. Combinations of large-amplitude oscillations and small- amplitude oscillations are obtained for the electric circuit, while combination of fast-slow dynamics is obtained for the mechani- cal part. The results of the paper provide potential criteria for evaluating and optimizing system performance.

Acknowledgments

This work is supported by the US Office of Naval Research under the grant ONR N00014-08-1-0435. Thanks are due to Mr Anthony Seman III of ONR and Dr. Stephen Mastro of NAVSEA, Philadelphia.

References

  1. [1]  Erturk, A. and Inman, D. (2011), Broadband piezoelectric power generation on high-energy orbits of the bistable duffing oscillator with electromechanical coupling, Journal of Sound and Vibration, 330(10), 2339 - 2353.
  2. [2]  Erturk, A. and Inman, D. (2011), Piezoelectric Energy Harvesting, John Wiley & Sons Ltd, Chichester, UK.
  3. [3]  Kwuimy, C.A.K., Litak, G., Borowiec, M., and Nataraj, C. (2012), Performance of a piezoelectric energy harvester driven by air fow, Applied Physics Letters, 100, 024103, 1-3.
  4. [4]  Zhang,W., Zu, J. and Wang, F. (2008), Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness, Chaos, Solitons and Fractals, 35(3), 586-608.
  5. [5]  Kwuimy, C.A.K. and Nataraj, C. (2012), Modeling and nonlinear dynamics analysis of a magnetically actuated butterfly valve, Nonlinear Dynamics, 70, 435-451.
  6. [6]  Nayfeh, A.H. and Mook, D. (1979), Nonlinear Oscillations, Wiley-Interscience, New York.
  7. [7]  Wiggins, S. (2000), Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-verlag, Berlin.
  8. [8]  Ji, Y. and Bi, Q. (2010), Bursting behavior in a non-smooth electric circuit, Physics Letters A, 374(13-14), 1434-1439.
  9. [9]  Kwuimy, C.A.K., Nataraj, C., and Litak, G. (2011), Melnikovs criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 21 (043113), 1-12.
  10. [10]  Simo, H. and Woafo, P. (2011), Bursting oscillations in electromechanical systems, Mechanics Research Communications, 38(8), 537-541.
  11. [11]  Abobda, L. and Woafo, P. (2012), Subharmonic and bursting oscillations of a ferromagnetic mass fixed on a spring and subjected to an ac electromagnet, Communications in Nonlinear Science and Numerical Simulation, 17 (7), 3082-3091.
  12. [12]  Carnevale, N.T. and Wachtel, H. (1980), Two reciprocating current components underlying slow oscillations in aplysia bursting neurons, Brain Research Reviews, 2 (1-3), 45 - 68.
  13. [13]  Haberichter, T., Marhl,M., and Heinrich, R. (2001), Birhythmicity, trirhythmicity and chaos in bursting calcium oscillations, Biophysical Chemistry, 90(1), 17 - 30.
  14. [14]  Ciss, Y., Nita, D., Steriade, M., and Timofeev, I. (2007), Callosal responses of fast-rhythmic-bursting neurons during slow oscillation in cats, Neuroscience, 147(2), 272 - 276.
  15. [15]  Ouyang, G., Li, X., Dang, C. and Richards, D.A. (2008), Using recurrence plot for determinism analysis of EEG recordings in genetic absence epilepsy rats, Clinical Neurophysiology, 119, 1747-1755.
  16. [16]  Han, X. and Bi, Q. (2011), Bursting oscillations in duffings equation with slowly changing external forcing, Communications in Nonlinear Science and Numerical Simulation, 16(10), 4146-4152.
  17. [17]  Naseradinmousavi, P. and Nataraj,C. (2011), Nonlinear mathematical modeling of butterfly valves driven by solenoid actuators, Applied Mathematical Modelling, 35, 2324-2335.
  18. [18]  Naseradinmousavi, P. and Nataraj, C., (2012), Transient chaos and crisis phenomena in butterfly valves driven by solenoid actuators, Communications in Nonlinear Science and Numerical Simulation, 17 (11), 4336-4345.
  19. [19]  Luongo, A. and Zulli, D. (2011), Parametric, external and self-excitation of a tower under turbulent wind flow, Journal of Sound and Vibration, 330 (13), 3057-3069.