The variational iteration method for nonlinear oscillators with discontinuities

Journal of Sound and Vibration

Volumn 305, Issue 4-5, 2007, Pages 614-620

  Rafei, M ^a   Ganji, D D ^a   Daniali, H ^a   Pashaei, H ^a  

^a UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; LINEARIZATION; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; VARIATIONAL TECHNIQUES;

APPROXIMATE SOLUTIONS; SOLUTION DOMAINS; VARIATIONAL ITERATION METHOD (VIM);

OSCILLATORS (MECHANICAL);

EID: 34447517053     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2007.04.020     Document Type: Article

References (39)

1. Nayfeh A.H. Introduction to Perturbation Techniques (1981), Wiley, New York
2. Bender C.M., Pinsky K.S., and Simmons L.M. A new perturbative approach to nonlinear problems. Journal of Mathematical Physics 30 7 (1989) 1447-1455
3. He J.H. A note on delta-perturbation expansion method. Applied Mathematics and Mechanics 23 6 (2002) 634-638
4. He J.H. Preliminary report on the energy balance for nonlinear oscillations. Mechanics Research Communications 29 2-3 (2002) 107-111
5. He J.H. Determination of limit cycles for strongly nonlinear oscillators. Physics Review Letter 90 17 (2003) 174301
6. He J.H. Variational iteration method: a kind of nonlinear analytical technique: some examples. International Journal of Nonlinear Mechanics 34 4 (1999) 699-708
7. Hafez Tari D.D., Ganji H., and Babazadeh. The application of He's variational iteration method to nonlinear equations arising in heat transfer. Physics Letters A 363 3 (2007) 213-217
8. Rafei M., Daniali H., and Ganji D.D. Variational iteration method for solving the epidemic model and the prey and predator problem. Applied Mathematics and Computation 186 2 (2007) 1701-1709
9. Ganji D.D., and Sadighi A. Application of He's methods to nonlinear coupled systems of reaction-diffusion equations. International Journal of Nonlinear Sciences and Numerical Simulation 7 4 (2006) 411-418
10. Xu L. Determination of limit cycle by He's parameter-expanding method for strongly nonlinear oscillators. Journal of Sound and Vibration 302 1-2 (2007) 178-184
11. Xu L. Variational principles for coupled nonlinear Schrödinger equations. Physics Letters A 359 6 (2006) 627-629
12. Ganji D.D. The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Physics Letters A 355 4-5 (2006) 337-341
13. Rafei M., Ganji D.D., Mohammadi Daniali H.R., and Pashaei H. Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations. Physics Letters A 364 (2007) 1-6
14. Rafei M., Ganji D.D., and Daniali H. Solution of the epidemic model by homotopy perturbation method. Applied Mathematics and Computation 187 2 (2007) 1056-1062
15. Ganji D.D., and Rafei M. Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method. Physics Letters A 356 2 (2006) 131-137
16. Rafei M., and Ganji D.D. Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation 7 3 (2006) 321-329
17. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Applied Mathematics and Computation 151 1 (2004) 287-292
18. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-linear Mechanics 35 1 (2000) 37-43
19. Özis T., and Yildirim A. A comparative study of He' homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 243-248
20. He J.H. Bookkeeping parameter in perturbation methods. International Journal of Non-Linear Sciences and Numerical Simulation 2 3 (2001) 257-264
21. He J.H. A review on some new recently developed nonlinear analytical techniques. International Journal of Nonlinear Sciences and Numerical Simulation 1 1 (2000) 51-70
22. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 20 10 (2006) 1141-1199
23. J.H. He, Non-perturbative Methods for Strongly Nonlinear Problems, Dissertation, de-Verlag im Internet GmbH, Berlin, 2006.
24. Liu H.-M. Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method. Chaos, Solitons and Fractals 23 (2005) 577-579
25. He J.H. Modified Lindstedt-Poincare methods for some strongly non-linear oscillators Part I. International Journal of Non-linear Mechanics 37 2 (2002) 309-314
26. He J.H. Modified Lindstedt-Poincare methods for some strongly non-linear oscillators Part II. International Journal of Non-linear Mechanics 37 2 (2002) 315-320
27. He J.H. Modified Lindstedt-Poincare methods for some strongly non-linear oscillators Part III. International Journal of Nonlinear Sciences and Numerical Simulation 2 4 (2001) 317-320
28. Beléndez A., Hernández A., Beléndez T., et al. Application of He's homotopy perturbation method to the Duffing-harmonic oscillator. International Journal of Nonlinear Sciences and Numerical Simulation 8 1 (2007) 79-88
29. He J.H. New interpretation of homotopy perturbation method. International Journal of Modern Physics B 20 18 (2006) 2561-2568
30. Shou D.-H., and He J.H. Application of parameter-expanding method to strongly nonlinear oscillators. International Journal of Nonlinear Sciences and Numerical Simulation 8 1 (2007) 121-124
31. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering 167 1-2 (1998) 57-68
32. Tari H., Ganji D.D., and Rostamian M. Approximate solutions of K(2,2), KdV and modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 203-210
33. Yusufoglu E. Variational iteration method for construction of some compact and noncompact structures of Klein-Gorden equations. International Journal of Nonlinear Sciences and Numerical Simulation 8 2 (2007) 153-158
34. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Sciences and Numerical Simulation 7 1 (2006) 27-34
35. Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations. International Journal of Nonlinear Sciences and Numerical Simulation 7 1 (2006) 65-70
36. Inokuti M., et al. General use of the Lagrange multiplier in non-linear mathematical physics. In: Nemat-Nasser S. (Ed). Variational Method in the Mechanics of Solids (1978), Pergamon Press, Oxford 156-162
37. He J.H. Semi-inverse method of establishing generalized principles for fluid mechanics with emphasis on turbomachinery aerodynamics. International Journal of Turbo Jet-Engines 14 1 (1997) 23-28
38. He J.H. Variational principles for some nonlinear partial differential equations with variable coefficient. Chaos, Solitons and Fractals 19 4 (2004) 847-851
39. Acton J.R., and Squire P.T. Solving Equations with Physical Understanding (1985), Adam Hilger Ltd., Bristol