PIER M
 
Progress In Electromagnetics Research M
ISSN: 1937-8726
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 4 > pp. 143-154

HE'S ENERGY BALANCE METHOD TO EVALUATE THE EFFECT OF AMPLITUDE ON THE NATURAL FREQUENCY IN NONLINEAR VIBRATION SYSTEMS

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

Full Article PDF (667 KB)

Abstract:
This paper presents a new approach for solving accurate approximate analytical solution for strong nonlinear oscillators. The new algorithm offers a promising approach by Hamiltonian for the nonlinear oscillator. We find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.

Citation:
H. Babazadeh, D. D. Ganji, and M. Akbarzade, "He's Energy Balance Method to Evaluate the Effect of Amplitude on the Natural Frequency in Nonlinear Vibration Systems," Progress In Electromagnetics Research M, Vol. 4, 143-154, 2008.
doi:10.2528/PIERM08071004

References:
1. 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

2. Bender, C. M., K. 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

3. 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

4. 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

5. 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

6. 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

7. 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.

8. 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

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

10. 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

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

12. 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

13. 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

14. 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 imulation, Vol. 7, No. 3, 321-329, 2006.

15. 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

16. 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

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

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

19. 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.

20. 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

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

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., "Homotopy perturbation method: A new nonlinear analytical technique," Applied Mathematics and Computation, Vol. 135, 73-79, 2003.
doi:10.1016/S0096-3003(01)00312-5

24. Arnold, M. D., "An efficient solution for scattering by a perfectly conducting strip grating," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 891-900, 2006.
doi:10.1163/156939306776149905

25. Zhao, J. X., "Numerical and analytical formulations of the extended MIE theory for solving the sphere scattering problem," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 967-983, 2006.
doi:10.1163/156939306776149815

26. Rui, P.-L. and R. Chen, "Implicity restarted gmres fast Fourier transform method for electromagnetic scattering," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 7, 973-976, 2007.
doi:10.1163/156939307780748968

27. Wang, M. Y., J. Xu, J. Wu, Y. Yan, and H.-L. Li, "FDTD study on scattering of metallic column covered by double negative metamaterial," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1905-1914, 2007.
doi:10.1163/156939307783152777

28. Liu, X.-F., B. Z. Wang, and S.-J. Lai, "Element-free Galerkin method in electromagnetic scattering field computation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1915-1923, 2007.
doi:10.1163/156939307783152920

29. Kumar, P., T. Chakravarty, S. Bhooshan, S. K. Khah, and A. De, "Numerical computation of resonant frequency of gap coupled circular microstrip antennas," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 10, 1303-1311, 2007.
doi:10.1163/156939307783239465

30. Ding, W., L. Chen, and C. H. Liang, "Numerical study of Goos-Hanchen shift on the surface of anisotropic left-handed materials," Progress In Electromagnetics Research B, Vol. 2, 151-164, 2008.
doi:10.2528/PIERB07111403

31. Popov, A. V. and V. V. Kopeikin, "Electromagnetic pulse propagation over nonuniform earth surface: Numerical simulation," Progress In Electromagnetics Research B, Vol. 6, 37-64, 2008.
doi:10.2528/PIERB08031102

32. Suyama, T., Y. Okuno, A. Matsushima, and M. Ohtsu, "A numerical analysis of stop band characteristics by multilayered dielectric gratings with sinusoidal profile," Progress In Electromagnetics Research B, Vol. 2, 83-102, 2008.
doi:10.2528/PIERB07110301

33. Mokari, H. and P. Derakhshan-Barjoei, "Numerical analysis of homojunction Gallium arsenide avalanche photodiodes (GAAs-APDs)," Progress In Electromagnetics Research B, Vol. 7, 159-172, 2008.
doi:10.2528/PIERB08032702

34. Steinbauer, M., R. Kubasek, and K. Bartusek, "Numerical method of simulation of material influences in MR tomography," Progress In Electromagnetics Research Letters, Vol. 1, 205-210, 2008.
doi:10.2528/PIERL07120605


© Copyright 2010 EMW Publishing. All Rights Reserved