Advertisement

Nonlinear Dynamics

, Volume 63, Issue 1–2, pp 35–49 | Cite as

Nonlinear dynamics of a new electro-vibro-impact system

  • Jee-Hou HoEmail author
  • Van-Du Nguyen
  • Ko-Choong Woo
Original Paper

Abstract

A variety of nonlinear dynamic responses for a new electro-vibro-impact system is presented, with indication of chaotic behavior. By mathematical modeling of the physical system, an insight is obtained to the global system dynamics. The modeling has established a good correlation with experimental data, and hence can be used as a numerical tool to optimize the system dynamics. In particular, with respect to impact forces and progression rate, may then be achieved with minimal computational cost.

Keywords

Electro-vibro-impact system Chaos Mathematical model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Wiercigroch, M.: Applied nonlinear dynamics of non-smooth mechanical systems. J. Braz. Soc. Mech. Sci. Eng. 28(4), 521–528 (2006) MathSciNetGoogle Scholar
  2. 2.
    Shaw, S.W., Holmes, P.J.: A periodically forced piecewise linear oscillator. J. Sound Vib. 90(1), 129–155 (1983) zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Pavlovskaia, E., Wiercigroch, M., Grebogi, C.: Modelling of an impact system with a drift. Phys. Rev. E 64, 056224 (2001) (9 pages) CrossRefGoogle Scholar
  4. 4.
    Wiercigroch, M., Sin, V.T.W.: Experimental study of base excited symmetrically piecewise linear oscillator. ASME J. Appl. Mech. 65(3), 657–663 (1998) CrossRefGoogle Scholar
  5. 5.
    Peterka, F., Vacik, J.: Transition to chaotic motion in mechanical systems with impacts. J. Sound Vib. 154(1), 95–115 (1992) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Peterka, F.: Bifurcations and transition phenomena in an impact oscillator. Chaos Solitons Fractals 7(10), 1635–1647 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Wiercigroch, M.: Modelling of dynamical systems with motion dependent discontinuities. Chaos Solitons Fractals 11(15), 2429–2442 (2000) zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Pavlovskaia, E., Wiercigroch, M.: Analytical drift reconstruction for visco-elastic impact oscillators operating in periodic and chaotic regimes. Chaos Solitons Fractals 19(1), 151–161 (2004) zbMATHCrossRefGoogle Scholar
  9. 9.
    Pavlovskaia, E., Wiercigroch, M.: Periodic solution finder for an impact oscillator with a drift. J. Sound Vib. 267(4), 893–911 (2003) CrossRefMathSciNetGoogle Scholar
  10. 10.
    Chatterjee, S., Mallik, A.K., Ghosh, A.: On impact dampers for non-linear vibrating systems. J. Sound Vib. 187(3), 403–420 (1995) CrossRefGoogle Scholar
  11. 11.
    Barrientos, G., Baeza, L.: Simulation of impact between rigid elements. Int. J. Solids Struct. 40(19), 4943–4954 (2003) zbMATHCrossRefGoogle Scholar
  12. 12.
    Hinrichs, N., Oestreich, M., Popp, K.: Dynamics of oscillators with impact and friction. Chaos Solitons Fractals 8(4), 535–558 (1997) zbMATHCrossRefGoogle Scholar
  13. 13.
    Hinrichs, N., Oestreich, M., Popp, K.: On the modeling of friction oscillators. J. Sound Vib. 216(3), 435–459 (1998) CrossRefGoogle Scholar
  14. 14.
    Davis, R.B., Virgin, L.N.: Non-linear behavior in a discretely forced oscillator. Int. J. Non-Linear Mech. 42(5), 744–753 (2007) CrossRefGoogle Scholar
  15. 15.
    Batako, A.D.L., Lalor, M.J., Piiroinen, P.T.: Numerical bifurcation analysis of a friction-driven vibro-impact system. J. Sound Vib. 308, 392–404 (2007) CrossRefGoogle Scholar
  16. 16.
    Piiroinen, P.T., Kuznetsov, Y.A.: An event-driven method to simulate Filippov systems with accurate computing of sliding motions. ACM Trans. Math. Softw. 34(3), Article 13 (2008) Google Scholar
  17. 17.
    Nguyen, V.-D., Woo, K.-C., Pavlovskaia, E.: Experimental study and mathematical modelling of a new of vibro-impact moling device. Int. J. Non-Linear Mech. 43(6), 542–550 (2008) CrossRefGoogle Scholar
  18. 18.
    Barkan, D.D.: Dynamics of Bases and Foundations. McGraw-Hill, New York (1962) Google Scholar
  19. 19.
    Rodger, A.A., Littlejohn, G.S.: A study of vibratory driving in granular soils. Geotechnique 30, 269–293 (1980) CrossRefGoogle Scholar
  20. 20.
    Nguyen, V.-D., Woo, K.-C.: Nonlinear dynamic responses of new electro-vibroimpact system. J. Sound Vib. 310, 769–775 (2008) CrossRefGoogle Scholar
  21. 21.
    Wiercigroch, M., Wojewoda, J., Krivtsov, A.M.: Dynamics of ultrasonic percussive drilling of hard rocks. J. Sound Vib. 280(3–5), 739–757 (2005) CrossRefGoogle Scholar
  22. 22.
    Wiercigroch, M., Sin, V.W.T., Liew, Z.F.K.: Non-reversible dry friction oscillator, design and measurements. Proc. Inst. Mech. Eng., Part C 213, 527–534 (1999) CrossRefGoogle Scholar
  23. 23.
    Mendrela, E.A., Pudlowski, Z.J.: Transients and dynamics in a linear reluctance self-oscillating motor. IEEE Trans. Energy Convers. 7(1), 183–191 (1992) CrossRefGoogle Scholar
  24. 24.
    Mendrela, E.A.: Comparison of the performance of a linear reluctance oscillating motor operating under ac supply with one under dc supply. IEEE Trans. Energy Convers. 14(3), 328–332 (1999) CrossRefGoogle Scholar
  25. 25.
    Nguyen, V.-D., Woo, K.-C.: Optimisation of a solenoid-actuated vibro-impact mechanism for ground moling machines. In: XXXV Summer School-Conference, Advanced Problems in Mechanics, St. Petersburg, Russia, June 20–28. APM (2007) Google Scholar
  26. 26.
    Woo, K.-C., Rodger, A.A., Neilson, R.D., Wiercigroch, M.: Application of the harmonic balance method to ground moling devices operating in periodic regimes. Chaos Solitons Fractals 11(15), 2515–2525 (2000) zbMATHCrossRefGoogle Scholar
  27. 27.
    Pavlovskaia, E., Wiercigroch, M., Woo, K.-C., Rodger, A.A.: Modelling of a vibro-impact ground moling system by an impact oscillator with a frictional slider. Meccanica 38(1), 85–97 (2003) zbMATHCrossRefGoogle Scholar
  28. 28.
    Wiercigroch, M.: A note on the switch function for the stick-slip phenomenon. J. Sound Vib. 175(5), 700–704 (1994) zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Pavlovskaia, E., Wiercigroch, M., Grebogi, C.: Two-dimensional map for impact oscillator with drift. Phys. Rev. E 70, 036201 (2004) (10 pages) Google Scholar
  30. 30.
    Wiercigroch, M., Pavlovskaia, E.: Low-dimensional maps for piecewise smooth oscillators. J. Sound Vib. 305(4–5), 750–771 (2007) MathSciNetGoogle Scholar
  31. 31.
    Błażejczyk-Okolewska, B., Czolczynski, K., Kapitaniak, T.: Classification principles of types of mechanical systems with impacts—fundamental assumptions and rules. Eur. J. Mech. A/Solids 23(3), 517–537 (2004) zbMATHCrossRefGoogle Scholar
  32. 32.
    Czolczynski, K., Kapitaniak, T.: Influence of the mass and stiffness ratio on a periodic motion of two impacting oscillators. Chaos Solitons Fractals 17, 1–110 (2003) zbMATHCrossRefGoogle Scholar
  33. 33.
    de Souza, S.L.T., Batista, A.M., Caldas, I.L., Viana, R.L., Kapitaniak, T.: Noise-induced basin hopping in a vibro-impact system. Chaos Solitons Fractals 32, 758–767 (2007) CrossRefGoogle Scholar
  34. 34.
    Wiercigroch, M., Sin, V.W.T., Li, K.-Y.: Measurement of chaotic vibration in a symmetrically piecewise linear oscillator. Chaos Solitons Fractals 9(1–2), 209–220 (1998) CrossRefGoogle Scholar
  35. 35.
    Lenci, S., Rega, G.: Regular nonlinear dynamics and bifurcations of an impacting system under general periodic excitation. Nonlinear Dyn. 34(3–4), 249–268 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Lenci, S., Rega, G.: Numerical control of impact dynamics of inverted pendulum through optimal feedback strategies. J. Sound Vib. 236(3), 505–527 (2000) CrossRefGoogle Scholar
  37. 37.
    Yorke, J.A., Nusse, H.E.: Dynamics: Numerical Explorations. Springer, New York (1998) Google Scholar
  38. 38.
    Crandall, S.H., et al.: In: Crandall, S.H. (ed.) Dynamics of Mechanical and Electromechanical Systems. McGraw-Hill, New York (1968) Google Scholar
  39. 39.
    Bryant, P.H.: LyapOde (Version 4), available online at http://inls.ucsd.edu/~pbryant/ (2009)
  40. 40.
    Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57(3), 617–656 (1985) CrossRefMathSciNetGoogle Scholar
  41. 41.
    Ho, J.-H., Woo, K.-C.: Bifurcations in an electro-vibroimpact system with friction. J. Theor. Appl. Mech. 46(3), 511–520 (2008) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Faculty of Engineering and ScienceUniversiti Tunku Abdul RahmanSetapakMalaysia
  2. 2.Thai Nguyen University of TechnologyThai Nguyen CityViet Nam
  3. 3.Faculty of EngineeringThe University of Nottingham Malaysia CampusSemenyihMalaysia

Personalised recommendations