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Progress In Electromagnetics Research C
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ANALYSIS OF NONLINEAR OSCILLATORS WITH U FORCE BY HE’S ENERGY BALANCE METHOD

By M. Akbarzade, D. D. Ganji, and M. H. Pashaei

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Abstract:
In this letter,an application of energy balance method is applied to solve the nonlinear oscillators with un force. Comparison is made between the modification of harmonic balance method and energy balance method. The results reveal that the energy balance method is very effective and simple. Energy balance method is very effective and convenient and quite accurate to both linear and nonlinear physics and engineering problems.

Citation:
M. Akbarzade, D. D. Ganji, and M. H. Pashaei, "Analysis of Nonlinear Oscillators with U Force by He’S Energy Balance Method," Progress In Electromagnetics Research C, Vol. 3, 57-66, 2008.
doi:10.2528/PIERC08032901

References:
1. Nayfe, A. H. and D. T. Mook, Nonlinear Oscillations, Wiley, New York, 1979.

2. He, J. H., "Preliminary report on the energy balance for nonlinear oscillations," Mechanics Research Communication, Vol. 29, 107-111, 2002.
doi:10.1016/S0093-6413(02)00237-9

3. Xu, L., "He’s parameter-expanding methods for strongly nonlinear scillators," Journal of Computation and Applied Mathematics, Vol. 207, 148-154, 2007.
doi:10.1016/j.cam.2006.07.020

4. Bender, C. M., S. Pinsky, and L. M. Simmons, "A new perturbative approach to nonlinear problems," Journal of Mathematical Physics, Vol. 30, No. 7, 1447-1455, 1989.
doi:10.1063/1.528326

5. He, J. H., "A note on delta-perturbation expansion method," Applied Mathematics and Mechanics, Vol. 23, No. 6, 634-638, 2002.
doi:10.1007/BF02437646

6. He, J. H., "Variational iteration method: A kind of nonlinear analytical technique: Some examples ," International Journal of Nonlinear Mechanics, Vol. 34, No. 4, 699-708, 1999.
doi:10.1016/S0020-7462(98)00048-1

7. Ganji, D. D., H. Tari, and H. Babazadeh, "The application of He’s variational iteration method to nonlinear equations arising in heat transfer," Physics Letters A, Vol. 363, No. 3, 213-217, 2007.
doi:10.1016/j.physleta.2006.11.005

8. Rafei, M., H. Daniali, and D. D. Ganji, "Variational iteration method for solving the epidemic model and the prey and predator problem," Applied Mathematics and Computation, Vol. 186, No. 2, 1701-1709, 2007.
doi:10.1016/j.amc.2006.08.077

9. Ganji, D. D. and A. Sadighi, "Application of He’s methods to nonlinear coupled systems of reaction-diffusion equations," International Journal of Nonlinear Sciences and Numerical Simulation , Vol. 7, No. 4, 411-418, 2006.

10. Xu, L, "Determination of limit cycle by He’s parameterexpanding method for strongly nonlinear oscillators," Journal of Sound and Vibration, Vol. 302, No. 1–2, 178-184, 2007.
doi:10.1016/j.jsv.2006.11.011

11. Xu, L., "Variational principles for coupled nonlinear Schro dinger equations," Physics Letters A , Vol. 359, No. 6, 627-629, 2006.
doi:10.1016/j.physleta.2006.07.026

12. Ganji, D. D., "The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer," Physics Letters A, Vol. 355, No. 4–5, 337-341, 2006.
doi:10.1016/j.physleta.2006.02.056

13. Rafei, M., D. D. Ganji, H. R. M. Daniali, and H. Pashaei, "Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations ," Physics Letters A, Vol. 364, 1-6, 2007.
doi:10.1016/j.physleta.2006.11.047

14. Rafei, M., D. D. Ganji, and H. Daniali, "Solution of the epidemic model by homotopy perturbation method," Applied Mathematics and Computation, Vol. 187, No. 2, 1056-1062, 2007.
doi:10.1016/j.amc.2006.09.019

15. Ganji, D. D. 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, 131-137, 2006.
doi:10.1016/j.physleta.2006.03.039

16. Rafei, M. and D. D. Ganji, "Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method ," International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, No. 3, 321-329, 2006.

17. He, J. H., "The homotopy perturbation method for nonlinear oscillators with discontinuities," Applied Mathematics and Computation, Vol. 151, No. 1, 287-292, 2004.
doi:10.1016/S0096-3003(03)00341-2

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, Vol. 35, No. 1, 37-43, 2000.
doi:10.1016/S0020-7462(98)00085-7

19. Ozis, T. and A. Yildirim, "A comparative study of He’s homotopy perturbation method for determining frequencyamplitude relation of a nonlinear oscillator with discontinuities ," International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8, No. 2, 243-248, 2007.

20. He, J. H., "Bookkeeping parameter in perturbation methods," International Journal of Non-linear Sciences and Numerical Simulation , Vol. 2, No. 3, 257-264, 2001.

21. He, J. H., "A review on some new recently developed nonlinear analytical techniques," International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 1, No. 1, 51-70, 2000.

22. He, J. H., "Some asymptotic methods for strongly nonlinear equations ," International Journal of Modern Physics B, Vol. 20, No. 10, 1141-1199, 2006.
doi:10.1142/S0217979206033796

23. He, J. H., "Non-perturbative methods for strongly nonlinear problems," Dissertation, de-Verlag im Internet GmbH, Berlin, 2006.

24. He, J. H., "Some asymptotic methods for strongly nonlinear equations ," International Journal of Modern Physics B, Vol. 20, No. 10, 1141-1199, 2006.
doi:10.1142/S0217979206033796


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