Analysis of vibration of pendulum arm under bursting oscillation excitation
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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.
KeywordsSingle pendulum arm double pendulum arms bursting oscillations nonlinear RLC circuit
PACS Nos01.40.gb 01.55.+b 01.40.gf 83.60.Np
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.
- 3.H Simo and P Woafo, Int. J. Birfuc. Chaos 22, 1 (2012)Google Scholar
- 5.P R Venkatesh and A Venkatesan, Pramana – J. Phys. 87(1): 3 (2016)Google Scholar
- 8.B Pal, D Dutta and S Poria, Pramana – J. Phys. 89: 32 (2016)Google Scholar
- 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.D Sado and K Gajos, J. Theor. Appl. Math. 46, 141 (2008)Google Scholar
- 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.D Yurchenko and P Alevras, Mech. Syst. Signal Process. 99(15), 515 (2018)Google Scholar
- 23.T Sze-Hong, W Ko-Choong and H Demrdash, J. Theor. Appl. Mech. 54(3), 730 (2016)Google Scholar
- 26.M E Izhikevich, Dyn. Syst. Neurosci. 50(2), 397 (2008)Google Scholar