Dynamic Analysis of Generalized Conservative Nonlinear Oscillators Via Frequency Amplitude Formulation

Arabian Journal for Science and Engineering

Volumn 38, Issue 1, 2013, Pages 175-179

  Khan, Y ^a   Kalami Yazdi, M ^b   Askari, H ^b   Saadatnia, Z ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Conservative nonlinear oscillators; Duffing equation; Frequency amplitude formulation; Plasma physics

Indexed keywords

EID: 84871968716     PISSN: 2193567X     EISSN: 21914281     Source Type: Journal    
DOI: 10.1007/s13369-011-0035-y     Document Type: Article

References (39)

1. Nayfeh A. H., Mook D. T.: Nonlinear Oscillations. Wiley, New York (1979).
2. Adomian G.: Solving Frontier Problems of Physics: The Decomposition Method. Kluwer, Boston (1994).
3. He J. H., Wu G.-C., Austin F.: The variational iteration method which should be followed. Nonlinear Sci. Lett. A. 1, 1-30 (2010).
4. He J. H.: Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Num. Simul. 6(2), 207-208 (2005).
5. Khan Y.: An effective modification of the Laplace decomposition method for nonlinear equations. Int. J. Nonlinear Sci. Num. Simul. 10(11-12), 1373-1376 (2009).
6. Khan Y., Wu Q.: Homotopy perturbation transform method for nonlinear equations using He's polynomials. Comput. Math. Appl. 61(8), 1963-1967 (2011).
7. He J. H.: Hamiltonian approach to nonlinear oscillators. Phys. Lett. A 374, 2312-2314 (2010).
8. Ahmadian H., Azizi H.: Stability analysis of a nonlinear jointed beam under distributed follower force. J. Vib. Cont. 17, 27-38 (2011).
9. Younesian D., Esmailzadeh E.: Vibration suppression of rotating beams using time-varying internal tensile force. J. Sound Vib. 330, 308-320 (2011).
10. Ahmadian H., Jalali H.: Identification of bolted lap joints parameters in assembled structures. Mech. Syst. Signal Process. 21, 1041-1050 (2007).
11. Khan Y., Faraz N.: A new approach to differential difference equations. J. Adv. Res. Differ. Equ. 2(2), 1-12 (2010).
12. Faraz N., Khan Y., Yildirim A.: Analytical approach to two-dimensional viscous flow with a shrinking sheet via variational iteration algorithm-II. J. King. Saud. Uni. Sci. 23, 77-81 (2011).
13. Ganji D. D., Babazadeh H., Noori F., Pirouz M. M., Janipour M.: An application of homotopy perturbation method for non-linear Blasius equation to boundary layer flow over a flat plate. Int. J. Nonlinear Sci. 7(4), 399-404 (2009).
14. Khan Y., Faraz N.: Application of modified Laplace decomposition method for solving boundary layer equation. J. King. Saud. Uni. Sci. 23, 115-119 (2011).
15. Xu, L.: A Hamiltonian approach for a plasma physics problem. Comput. Math. Appl. (2010). doi: 10. 1016/j. camwa. 2010. 06. 028.
16. He J. H.: Max-Min approach to nonlinear oscillators. Int. J. Nonlinear Sci. Num. Simul. 9(2), 207-210 (2008).
17. He J. H.: Variational approach for nonlinear oscillators. Chaos Solitons Fract. 34, 1430-1439 (2007).
18. Shou D. H., He J. H.: Application of parameter-expanding method to strongly nonlinear oscillators. Int. J. Nonlinear Sci. Num. Simul. 8(1), 121-124 (2007).
19. He, J. H.: Iteration perturbation method for strongly nonlinear oscillations. J. Vib. Cont. 7, 631. doi: 10. 1177/107754630100700501(2001).
20. Darvishi M. T., Kheybari S., Yildirim A.: Application of He's parameter-expansion method to a system of two van der Pol oscillators coupled via a Bath. Nonlinear Sci. Lett. A 1, 399-405 (2010).
21. Özis T., Yildirim A.: Generating the periodic solutions for forcing van der Pol oscillators by the iteration perturbation method. Nonlinear Anal. R. World. Appl. 10, 1984-1989 (2009).
22. Zeng D. Q., Lee Y. Y.: Analysis of strongly nonlinear oscillator using the max-min approach. Int. J. Nonlinear Sci. Num. Simul. 10, 1361-1368 (2009).
23. He J. H.: Comment on 'He's frequency formulation for nonlinear oscillators'. Eur. J. Phys. 29, L19-L22 (2008).
24. He J. H.: An improved amplitude-frequency formulation for nonlinear oscillators. Int. J. Nonlinear Sci. Num. Simul. 9(2), 211-212 (2008).
25. Younesian D., Askari H., Saadatnia Z., Kalami Yazdi M.: Frequency analysis of strongly nonlinear generalized Duffing oscillators using He's frequency-amplitude formulation and He's energy balance method. Comput. Math. Appl. 59, 3222-3228 (2010).
26. Zhang Y. N., Xu F., Deng L. L.: Exact solution for nonlinear Schrödinger equation by He's frequency formulation. Comput. Math. Appl. 58, 2449-2451 (2009).
27. Geng L., Cai X.-C.: He's frequency formulation for nonlinear oscillators. Eur. J. Phys. 28, 923-931 (2007).
28. Ren, Z.-F.; Gui, W.-K.: He's frequency formulation for nonlinear oscillators using a golden mean location. Comput. Math Appl. (2010). doi: 10. 1016/j. camwa. 2010. 08. 047.
29. Cai X.-C., Wu W.-Y.: He's frequency formulation for the relativistic harmonic oscillator. Comput. Math. Appl. 58, 2358-2359 (2009).
30. Zhao L.: He's frequency-amplitude formulation for nonlinear oscillators with an irrational force. Comput. Math. Appl. 58, 2477-2479 (2009).
31. Ren Z. F., Liu G. Q., Kang Y. X. et al.: Application of He's amplitude-frequency formulation to nonlinear oscillators with discontinuities. Phys. Scr. 80, 045003 (2009).
32. Cai, X.-C.; Liu, J.-F.: Application of the modified frequency formulation to a nonlinear oscillator. Comput. Math. Appl. (2010). doi: 10. 1016/j. camwa. 2010. 09. 025.
33. Kalami Yazdi M., Khan Y., Madani M., Askari H., Saadatnia Z., Yildirim A.: Analytical solutions for autonomous conservative nonlinear oscillator. Int. J. Nonlinear Sci. Num. Simul. 11, 979-984 (2010).
34. -1=0. J. Sound Vib. 306, 968-972 (2007).
35. Acton, J. R.; Squire, P. T.: Solving Equations with Physical Understanding, chap. 5. Adam Hilger, Bristol (1985).
36. Mickens R. E.: Oscillations in Planar Dynamic Systems. World Scientific, Singapore (1996).
37. Belendez A., Mendez D. I., Belendez T., Hernandez A., Alvarez M. L.: Harmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable. J. Sound Vib. 314, 775-782 (2008).
38. Ramos J. I.: Generalized decomposition methods for singular oscillators. Chaos Solitons Fractals 42, 1149-1155 (2009).
39. Ramos J. I.: An artificial parameter Linstedt-Poincare method for the periodic solutions of nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable. J. Sound Vib. 318, 1281-1290 (2008).