Advertisement

Pramana

, 92:3 | Cite as

Analysis of vibration of pendulum arm under bursting oscillation excitation

  • Herve SimoEmail author
  • Ulrich Simo Domguia
  • Jayanta Kumar Dutt
  • Paul Woafo
Article
  • 32 Downloads

Abstract

We investigate numerically the responses of the single pendulum and double pendulum arms coupled to a nonlinear RLC-circuit shaker through a magnetic field. These systems can be used to build a robotic device or an automat. The nonlinear RLC circuit is a Duffing oscillator that generates electric bursting oscillations. We first examine the dynamical behaviour of the single pendulum arm. Time series shows that the pendulum arm exhibits bursting oscillation. When the natural frequency \(w_2 <1\), the shape of the bursting in the electrical part is different from that observed in the pendulum arm and if \(w_2 >1\), the shape is the same. We then explore the behaviour of a double pendulum arm powered by electric bursting oscillations. Time series are also used to explore the behaviour of each pendulum arm. The results show that the displacement of each pendulum arm undergoes bursting oscillations resulting from the transfer of the electronic signal. The shape of bursting of the first pendulum is different from that of the second pendulum for some values of \(w_1 \). The shape, period and amplitude of the bursting oscillations depend on various control parameters.

Keywords

Single pendulum arm double pendulum arms bursting oscillations nonlinear RLC circuit 

PACS Nos

01.40.gb 01.55.+b 01.40.gf 83.60.Np 

Notes

Acknowledgements

Part of this work was done at the Indian Institute of Technology Delhi (IIT Delhi, India) during the research stay of H Simo. H Simo is grateful for the financial support provided by the C V Raman International Fellowship for African researchers under the ‘Visiting Fellowship’ scheme.

References

  1. 1.
    J Yang, Y P Xiong and J T Xing, Mech. Syst. Signal. Process. 45(2), 563 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    H K Roy, A S Das and J K Dutt, Mech. Mach. Theory  98, 48 (2016)CrossRefGoogle Scholar
  3. 3.
    H Simo and P Woafo, Int. J. Birfuc. Chaos 22, 1 (2012)Google Scholar
  4. 4.
    Y S Kondji, K G Fautso and P Woafo, Phys. Scr. 81, 015010 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    P R Venkatesh and A Venkatesan, Pramana – J. Phys. 87(1): 3 (2016)Google Scholar
  6. 6.
    B Qinsheng, C Xiaoke, K Juergen and Z Zhengdi, Nonlinear Dyn. 85, 2233 (2016)CrossRefGoogle Scholar
  7. 7.
    C A Chamgoué, R Yamapi and P Woafo, Eur. Phys. J. Plus 127, 59 (2012)CrossRefGoogle Scholar
  8. 8.
    B Pal, D Dutta and S Poria, Pramana – J. Phys. 89: 32 (2016)Google Scholar
  9. 9.
    G S M Ngueteu and P Woafo, Mech. Res. Commun. 46, 20 (2012)CrossRefGoogle Scholar
  10. 10.
    K C A Kitio, B Nana and P Woafo, J. Sound. Vib. 329(15), 3137 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    A C J Luo and F Wang, Commun. Nonlinear Sci. Numer. Simul. 7(1), 31 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    N G S Mbouna, R Yamapi and P Woafo, Commun. Nonlinear Sci. Numer. Simul. 13(7), 1213 (2008)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    T Sze-Hong, C Kok-Hong, W Ko-Choong and D Hazem, Int. J. Nonlinear Mech. 70, 73 (2015)CrossRefGoogle Scholar
  14. 14.
    M J Clifford and S R Bishop, Phys. Lett. A 201, 191 (1995)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    M J Clifford and S R Bishop, J. Aust. Math. Soc. B – Appl. Math. 37, 309 (1996)CrossRefGoogle Scholar
  16. 16.
    J L P Felix, J M Balthazar and R M L R F Brasil, J. Vib. Control 11(1), 121 (2005)CrossRefGoogle Scholar
  17. 17.
    H A Rafael, A N Hélio, M L R R B Reyolando, M B José, A B Madureira and M T Angelo, Meccanica 51(6), 1301 (2015)Google Scholar
  18. 18.
    D Sado and K Gajos, J. Theor. Appl. Math. 46, 141 (2008)Google Scholar
  19. 19.
    M T Angelo, V Piccirillo, M B Actila, J M Balthazar, S Danuta, L P F Jorge and R L R F B Manoel, J. Vib. Control 1, 17 (2015)Google Scholar
  20. 20.
    D Yurchenko and P Alevras, Mech. Syst. Signal Process. 99(15), 515 (2018)Google Scholar
  21. 21.
    P Alevras, I Brown and D Yurchenko, Nonlinear Dyn. 81(1), 201(2015)CrossRefGoogle Scholar
  22. 22.
    T Sze-Hong, W Ko-Choong and H Demrdash, J. Comput. Nonlinear. Dyn. 13(1), 011006 (2017)CrossRefGoogle Scholar
  23. 23.
    T Sze-Hong, W Ko-Choong and H Demrdash, J. Theor. Appl. Mech. 54(3), 730 (2016)Google Scholar
  24. 24.
    S T Kingni, B Nana, M G S Ngueuteu, P Woafo and J Danckaert, Chaos Solitons Fractals 71, 29 (2015)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    H Xiujing, J Bo and Q S Bi, Nonlinear Dyn. 61(4), 667 (2010)CrossRefGoogle Scholar
  26. 26.
    M E Izhikevich, Dyn. Syst. Neurosci. 50(2), 397 (2008)Google Scholar
  27. 27.
    Q S Bi and Z D Zhang, Phys. Lett. A 3750, 1183 (2011)ADSCrossRefGoogle Scholar
  28. 28.
    O Decroly and A Goldebeter, J. Theor. Biol. 124, 219 (1987)CrossRefGoogle Scholar
  29. 29.
    Q Bi, C Xiaoke, K Juergen and Z Zhengdi, Nonlinear Dyn. 85(4), 2233 (2016)CrossRefGoogle Scholar
  30. 30.
    H Simo and P Woafo, Optik 127(20), 8760 (2016)ADSCrossRefGoogle Scholar
  31. 31.
    L T Abobda and P Woafo, Commun. Nonlinear Sci. Numer. Simul. 17(7), 3082 (2012)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    U Simo Domguia, L T Abobda and P Woafo, J. Comput. Nonlinear Dyn. 11(5), 051006 (2016)CrossRefGoogle Scholar
  33. 33.
    H Simo and P Woafo, Mech. Res. Commun. 38(8), 537 (2011)CrossRefGoogle Scholar
  34. 34.
    U Simo Domguia, M V Tchakui, H Simo and P Woafo, J. Vib. Acoust. 136(6), 061017 (2017)CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  • Herve Simo
    • 1
    • 2
    Email author
  • Ulrich Simo Domguia
    • 1
  • Jayanta Kumar Dutt
    • 2
  • Paul Woafo
    • 1
  1. 1.Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, Faculty of ScienceYaoundéCameroon
  2. 2.Department of Mechanical EngineeringIndian Institute of Technology DelhiHauz Khas, New DelhiIndia

Personalised recommendations