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Linked References

1. M. Mond, G. Cederbaum, P. B. Khan, and Y. Zarmi, “Stability analysis of the nonlinear Mathieu equation,” Journal of Sound and Vibration, vol. 167, no. 1, pp. 77–89, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
2. E. Esmailzadeh, G. Nakhaie-Jazar, and B. Mehri, “Existence of periodic solution for beams with harmonically variable length,” Journal of Vibration and Acoustics, vol. 119, no. 3, pp. 485–488, 1997. View at Publisher · View at Google Scholar
3. E. Esmailzadeh and N. Jalili, “Parametric response of cantilever Timoshenko beams with tip mass under harmonic support motion,” International Journal of Non-Linear Mechanics, vol. 33, no. 5, pp. 765–781, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
4. E. Esmailzadeh and A. Goodarzi, “Stability analysis of a CALM floating offshore structure,” International Journal of Non-Linear Mechanics, vol. 36, no. 6, pp. 917–926, 2001. View at Publisher · View at Google Scholar
5. Y. O. El-Dib, “Nonlinear Mathieu equation and coupled resonance mechanism,” Chaos, Solitons & Fractals, vol. 12, no. 4, pp. 705–720, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
6. L. Ng and R. Rand, “Bifurcations in a Mathieu equation with cubic nonlinearities,” Chaos, Solitons & Fractals, vol. 14, no. 2, pp. 173–181, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
7. L. Ng and R. Rand, “Bifurcations in a Mathieu equation with cubic nonlinearities—part II,” Communications in Nonlinear Science and Numerical Simulation, vol. 7, no. 3, pp. 107–121, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
8. J. F. Rhoads, S. W. Shaw, K. L. Turner, J. Moehlis, B. E. DeMartini, and W. Zhang, “Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators,” Journal of Sound and Vibration, vol. 296, no. 4-5, pp. 797–829, 2006. View at Publisher · View at Google Scholar
9. V. N. Belovodsky, S. L. Tsyfansky, and V. I. Beresnevich, “The dynamics of a vibromachine with parametric excitation,” Journal of Sound and Vibration, vol. 254, no. 5, pp. 897–910, 2002. View at Publisher · View at Google Scholar
10. G. T. Abraham and A. Chatterjee, “Approximate asymptotics for a nonlinear Mathieu equation using harmonic balance based averaging,” Nonlinear Dynamics, vol. 31, no. 4, pp. 347–365, 2003. View at Zentralblatt MATH · View at MathSciNet
11. M. Wiegand, S. Scheithauer, and S. Theil, “Step proof mass dynamics,” Acta Astronautica, vol. 54, no. 9, pp. 631–638, 2004. View at Publisher · View at Google Scholar
12. W. Zhang, R. Baskaran, and K. L. Turner, “Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor,” Sensors and Actuators A, vol. 102, no. 1-2, pp. 139–150, 2002. View at Publisher · View at Google Scholar
13. D. Younesian, E. Esmailzadeh, and R. Sedaghati, “Existence of periodic solutions for the generalized form of Mathieu equation,” Nonlinear Dynamics, vol. 39, no. 4, pp. 335–348, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
14. L. Cveticanin, “Vibrations in a parametrically excited system,” Journal of Sound and Vibration, vol. 229, no. 2, pp. 245–271, 2000. View at Publisher · View at Google Scholar
15. G. N. Jazar, “Stability chart of parametric vibrating systems using energy-rate method,” International Journal of Non-Linear Mechanics, vol. 39, no. 8, pp. 1319–1331, 2004. View at Publisher · View at Google Scholar
16. L. Cveticanin and I. Kovacic, “Parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity,” Journal of Sound and Vibration, vol. 304, no. 1-2, pp. 201–212, 2007. View at Publisher · View at Google Scholar
17. R. Bellman, Perturbation Techniques in Mathematics, Physics and Engineering, Holt, Rinehart and Winston, New York, NY, USA, 1964. View at Zentralblatt MATH · View at MathSciNet
18. J. D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell, Waltham, Mass, USA, 1968. View at Zentralblatt MATH · View at MathSciNet
19. R. E. O'Malley, Jr., Introduction to Singular Perturbations, Applied Mathematics and Mechanics, Academic Press, New York, NY, USA, 1974. View at Zentralblatt MATH · View at MathSciNet
20. J.-H. He, “Variational iteration method: a kind of nonlinear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. J.-H. He, “Variational iteration method—some recent results and new interpretations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 3–17, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
22. J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
23. J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for nonlinear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
24. J.-H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
25. I. Khatami, N. Tolou, J. Mahmoudi, and M. Rezvani, “Application of homotopy analysis method and variational iteration method for shock wave equation,” Journal of Applied Sciences, vol. 8, no. 5, pp. 848–853, 2008. View at Zentralblatt MATH · View at MathSciNet
26. M. Rafei, D. D. Ganji, H. Daniali, and H. Pashaei, “The variational iteration method for nonlinear oscillators with discontinuities,” Journal of Sound and Vibration, vol. 305, no. 4-5, pp. 614–620, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
27. N. Tolou, D. D. Ganji, M. J. Hosseini, and Z. Z. Ganji, “Application of homotopy perturbation method in nonlinear heat diffusion-convection-reaction equations,” The Open Mechanics Journal, vol. 1, no. 1, pp. 20–25, 2007. View at Publisher · View at Google Scholar
28. N. Tolou, I. Khatami, B. Jafari, and D. D. Ganji, “Analytical solution of nonlinear vibrating systems,” American Journal of Applied Sciences, vol. 5, no. 9, pp. 1219–1224, 2008. View at Zentralblatt MATH · View at MathSciNet
29. D. D. Ganji, M. Nourollahi, and E. Mohseni, “Application of He's methods to nonlinear chemistry problems,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 1122–1132, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
30. D. D. Ganji and M. Rafei, “Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method,” Physics Letters A, vol. 356, no. 2, pp. 131–137, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
31. A. Sadighi and D. D. Ganji, “Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods,” Physics Letters A, vol. 367, no. 1-2, pp. 83–87, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
32. F. Shakeri and M. Dehghan, “Inverse problem of diffusion equation by He's homotopy perturbation method,” Physica Scripta, vol. 75, no. 4, pp. 551–556, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
33. M. Dehghan and F. Shakeri, “Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method,” Progress in Electromagnetics Research, vol. 78, pp. 361–376, 2008. View at Publisher · View at Google Scholar
34. F. Shakeri and M. Dehghan, “Solution of delay differential equations via a homotopy perturbation method,” Mathematical and Computer Modelling, vol. 48, no. 3-4, pp. 486–498, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
35. A. Beléndez, C. Pascual, A. Márquez, and D. I. Méndez, “Application of He's homotopy perturbation method to the relativistic (An)harmonic oscillator—I: comparison between approximate and exact frequencies,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 4, pp. 483–492, 2007. View at Zentralblatt MATH · View at MathSciNet
36. A. Beléndez, C. Pascual, D. I. Méndez, M. L. Álvarez, and C. Neipp, “Application of He's homotopy perturbation method to the relativistic (An)harmonic oscillator—II: a more accurate approximate solution,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 4, pp. 493–504, 2007. View at Zentralblatt MATH · View at MathSciNet
37. A. Beléndez, A. Hernández, T. Beléndez, E. Fernández, M. L. Álvarez, and C. Neipp, “Application of He's homotopy perturbation method to the Duffing-harmonic oscillator,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 1, pp. 79–88, 2007. View at Zentralblatt MATH · View at MathSciNet
38. M. El-Shahed, “Application of differential transform method to nonlinear oscillatory systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1714–1720, 2008. View at Publisher · View at Google Scholar
39. M. L. James, G. M. Smith, and J. C. Wolford, Applied Numerical Methods for Digital Computation, Harper & Row, New York, NY, USA, 1985. View at Zentralblatt MATH · View at MathSciNet