Abstract
In this paper an electromechanical system is analyzed. The existence and asymptotic stability of a periodic orbit are obtained in a mathematically rigorous way as well as an expansion of the period by using an adequate small parameter. For the analytical results the main tool used is the regular perturbation theory. Some results, such as the growing of the period according to some powers of the parameters and the relation 2:1 between the period of the cart, which is a part of the electromechanical system, and the period of the current, are compatible with earlier numerical findings.
Similar content being viewed by others
References
Rocard, Y.: Dynamique Générale des Vibrations. Masson et Cie, Éditeurs, Paris, France, 459 pp (1943)
Kononenko, V.O.: Vibrating Systems with a Limited Power Supply, 236 pp. London Iliffe Books Ltd., England (1969)
Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations, 720 pp. Wiley, New York (1979)
Fidlin, A.: Nonlinear Oscillations in Mechanical Engineering, 358 pp. Springer, The Netherlands (2006)
Hagedorn, P.: Non-linear Oscillations, 300 pp. Clarendon, Oxford (1988)
Evan-Iwanowski, R.M.: Resonance Oscillations in Mechanical Systems, 306 pp. Elsevier, Amsterdam (1979)
Cartmell, M.: Introduction to Linear, Parametric and Nonlinear Vibrations, 260 pp. Springer, London (1990)
Awrejcewicz, J., Koruba, Z.: Classical Mechanics, Applied Mechanics and Mechatronics. Springer, New York (2012)
Dantas, M.J.H., Sampaio, R., Lima, R.A.: A nonlinear electromechanical system with stable periodic orbits. In: Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, J. (eds.) Dynamical Systems: Applications, pp. 353–364
Lima, R., Sampaio, R.: Analysis of an electromechanic coupled system with embarked mass. Mech Comput XXXI, 2709–2733 (2012)
Karnopp, D.C., Margolis, D.L., Rosenberg, R.C.: System Dynamics: Modeling and Simulation of Mechatronic Systems, 648 pp. Wiley, New-York (2006)
Lacarbonara, W., Antman, S.: What is Parametric Excitation in Structural Dynamics?. ENOC, Saint Petersburg (2008)
Hale, J.: Ordinary Differential Equations, 361 pp. Dover, Mineola, New York (2009)
Cronin, J.: Ordinary Differential Equations, 381 pp. Chapman & Hall/CRC, Boca Raton (2008)
Acknowledgments
The first author acknowledges the support given by FAPEMIG and the second and third authors acknowledge the support given by FAPERJ, CNPq, and CAPES.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dantas, M.J.H., Sampaio, R. & Lima, R. Asymptotically stable periodic orbits of a coupled electromechanical system. Nonlinear Dyn 78, 29–35 (2014). https://doi.org/10.1007/s11071-014-1419-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-014-1419-9