Abstract
An electromechanical system with flexible arm is considered. The mechanical part is a linear flexible beam and the electrical part is a nonlinear self-sustained oscillator. Oscillatory solutions are obtained using an averaging method. Chaotic behavior is studied via the Lyapunov exponent. The synchronization of regular and chaotic states of two such devices is discussed and the stability boundaries for the synchronization process are derived using the Floquet theory. We compare the results obtained from a finite difference simulation to those from the classical modal approach.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Chedjou, J.C., Woafo, P., Domngang, S.: Shilnikov chaos and dynamics of a self-sustained electromechanical transducer. ASME J. Vib. Acoust. 123, 170–174 (2001)
Yamapi, R., Woafo, P.: Dynamics and synchronization of self-sustained electromechanical devices. J. Sound Vib. 285, 1151–1170 (2005)
Kitio Kwuimy, C.A., Woafo, P.: Dynamics of a self-sustained electromechanical system with flexible arm and cubic coupling. Commun. Nonlinear Sci. Numer. Simul. 12, 1504–1517 (2007)
Jerrelind, J., Stensson, A.: Nonlinear dynamics of parts in engineering systems. Chaos Solitons Fractals 11, 2413–2428 (2000)
Chembo Kouomou, Y., Woafo, P.: Triple resonant states and chaos control in an electrostatic transducer with two outputs. J. Sound Vib. 270, 75–92 (2004)
Luo, A.C.J., Wang, F.Y.: Nonlinear dynamics of a micro-electromechanical system with time-varying capacitors. ASME J. Vib. Acoust. 126, 77–83 (2004)
Yamapi, R., Moukam Kakmeni, F.M., Chabi Orou, J.B.: Nonlinear dynamics and synchonization of coupled electromechanical systems with multiple functions. Commun. Nonlinear Sci. Numer. Simul. 12, 543–567 (2007)
Yamapi, R., Woafo, P.: Synchronized states in a ring of four mutually coupled self-sustained electromechanical devices. Commun. Nonlinear Sci. Numer. Simul. 11, 186–202 (2006)
Raskin, J.P., Brown, A.R., Khuri-Yakub, B.T., Rebeiz, G.M.: A novel parameter MEMS amplifier. J. Microelectromech. Syst. 9, 528–537 (2000)
Teufel, A., Steindl, A., Troger, H.: Synchronization of two flow excited pendula. Commun. Nonlinear Sci. Numer. Simul. 11, 577–594 (2006)
Bowong, S.: Adaptive synchronization between two different chaotic dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 12, 976–985 (2007)
Dibakar, G., Papri, S., Roy Chowdhury, A.: On synchronization of a forced delay dynamical system via the Galerkin approximation. Commun. Nonlinear Sci. Numer. Simul. 12, 928–941 (2007)
Dibakar, G., Roy Chowdhury, A., Papri, S.: On the various kinds of synchronization in delayed Duffing–Van der Pol system. Commun. Nonlinear Sci. Numer. Simul. 13, 790–803 (2008)
Oksasoglu, A., Vavriv, D.: Interaction of low and high-frequency oscillations in a nonlinear RLC circuit. IEEE Trans. Circuits Syst. 41, 669–672 (1994)
Hasler, M.J.: Electrical circuit with chaotic behaviour. Proc. IEEE 75, 1009–1021 (1987)
King, G.P., Gaito, S.T.: Bistable chaos, I, unfolding the cusp. Phys. Rev. A 46, 3092–3099 (1992)
Timoshenko, S., Gere, J.M.: Theory of Elastic Stability, 2nd edn. McGraw-Hill, New York (1961)
Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)
Hayashi, C.: Nonlinear Oscillations in Physical Systems. McGraw-Hill, New York (1964)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kitio Kwuimy, C.A., Woafo, P. Dynamics, chaos and synchronization of self-sustained electromechanical systems with clamped-free flexible arm. Nonlinear Dyn 53, 201–213 (2008). https://doi.org/10.1007/s11071-007-9308-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-007-9308-0