Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 670845, 11 pages
http://dx.doi.org/10.1155/2013/670845
Research Article

Equivalent Mathematical Representation of Second-Order Damped, Driven Nonlinear Oscillators

Centro de Innovación en Diseño y Tecnología, Tecnológico de Monterrey, Campus Monterrey E. Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico

Received 20 May 2013; Accepted 5 September 2013

Academic Editor: Hossein Jafari

Copyright © 2013 Alex Elías-Zúñiga and Oscar Martínez-Romero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Elías-Zúñiga, O. Martínez-Romero, and R. K. Córdoba-Díaz, “Approximate solution for the Duffing-harmonic oscillator by the enhanced cubication method,” Mathematical Problems in Engineering, Article ID 618750, 12 pages, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Beléndez, M. L. Lvarez, E. Fernndez, and I. Pascual, “Cubication of conservative nonlinear oscillators,” European Journal of Physics, vol. 30, no. 5, pp. 973–981, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Beléndez, D. I. Méndez, E. Fernández, S. Marini, and I. Pascual, “An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 373, no. 32, pp. 2805–2809, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Beléndez, G. Bernabeu, J. Francés, D. I. Méndez, and S. Marini, “An accurate closed-form approximate solution for the quintic Duffing oscillator equation,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 637–641, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Elías-Zúñiga, “A general solution of the Duffing equation,” Nonlinear Dynamics, vol. 45, no. 3-4, pp. 227–235, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. S. Siewe and U. H. Hegazy, “Homoclinic bifurcation and chaos control in MEMS resonators,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 35, no. 12, pp. 5533–5552, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Taylan, “The effect of nonlinear damping and restoring in ship rolling,” Ocean Engineering, vol. 27, no. 9, pp. 921–932, 2000. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Jeyakumari, V. Chinnathambi, S. Rajasekar, and M. A. F. Sanjuan, “Analysis of vibrational resonance in a quintic oscillator,” Chaos, vol. 19, no. 4, Article ID 043128, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. E. I. Butikov, “Extraordinary oscillations of an ordinary forced pendulum,” European Journal of Physics, vol. 29, no. 2, pp. 215–233, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. V. N. Pilipchuk, “Analytical study of vibrating systems with strong non-linearities by employing saw-tooth time transformations,” Journal of Sound and Vibration, vol. 192, no. 1, pp. 43–64, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. I. Kovacic, “Forced vibrations of oscillators with a purely nonlinear power-form restoring force,” Journal of Sound and Vibration, vol. 330, no. 17, pp. 4313–4327, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. A. K. Mallik, V. Kher, M. Puri, and H. Hatwal, “On the modelling of non-linear elastomeric vibration isolators,” Journal of Sound and Vibration, vol. 219, no. 2, pp. 239–253, 1999. View at Google Scholar · View at Scopus
  13. J. L. Trueba, J. Rams, and M. A. F. Sanjuán, “Analytical estimates of the effect of nonlinear damping in some nonlinear oscillators,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 10, no. 9, pp. 2257–2267, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Alex Elías-Zúñiga and Oscar Martínez-Romero, “Accurate solutions of conservative nonlinear oscillators by the enhanced cubication method,” Mathematical Problems in Engineering, vol. 2013, Article ID 842423, 9 pages, 2013. View at Publisher · View at Google Scholar
  15. Alex Elías-Zúñiga and Oscar Martínez-Romero, “Investigation of the equivalent representation form of strongly damped nonlinear oscillators by a nonlinear transformation approach,” Journal of Applied Mathematics, vol. 2013, Article ID 245092, 7 pages, 2013. View at Publisher · View at Google Scholar