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High conservative nonlinear vibration equations by means of energy balance method
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  • Journal title : Earthquakes and Structures
  • Volume 11, Issue 1,  2016, pp.129-140
  • Publisher : Techno-Press
  • DOI : 10.12989/eas.2016.11.1.129
 Title & Authors
High conservative nonlinear vibration equations by means of energy balance method
Bayat, Mahmoud; Pakar, Iman; Bayat, Mahdi;
 Abstract
This paper presents He`s Energy Balance Method (EBM) for solving nonlinear oscillatory differential equations. Three strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with numerical solutions using Runge-Kutta`s algorithm. The effects of different important parameters on the nonlinear response of the systems are studied. The results show the presented method is potentially to solve high nonlinear vibration equations.
 Keywords
Energy Balance Method (EBM);Runge- Kutta`s Method (RKM);nonlinear vibrations;
 Language
English
 Cited by
 References
1.
Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. crossref(new window)

2.
Andrianov, I.V., Awrejcewicz, J. and Manevitch, L.I. (2004), Asymptotical Mechanics of thin-walled Structures, Springer - Verlag Berlin Heidelberg, Germany.

3.
Atmane, H.A., Tounsi, A., Ziane, N. and Mechab, I. (2011), "Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section", Steel Compos. Struct., 11(6), 489-504. crossref(new window)

4.
Bayat, M. and Pakar, I. (2013a), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52. crossref(new window)

5.
Bayat, M. and Pakar, I. (2012a), "Accurate analytical solution for nonlinear free vibration of beams", Struct. Eng. Mech., 43(3), 337-347. crossref(new window)

6.
Bayat, M., Pakar, I. and Domaiirry, G. (2012b), "Recent developments of Some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: A review", Latin Am. J. Solid. Struct., 9(2), 145-234 .

7.
Bayat, M., Pakar, I. and Cveticanin, L. (2014d), "Nonlinear free vibration of systems with inertia and static type cubic nonlinearities : an analytical approach", Mechanism Machine Theory, 77, 50-58. crossref(new window)

8.
Bayat, M., Pakar, I. and Cveticanin, L. (2014e), "Nonlinear vibration of stringer shell by means of extended Hamiltonian approach", Arch. Appl. Mech., 84(1), 43-50. crossref(new window)

9.
Bayat, M. and Pakar, I. (2013c), "Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses", Earthq. Eng. Eng. Vib., 12(3), 411-420. crossref(new window)

10.
Bayat, M., Pakar, I. and Bayat, M. (2013b), "Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell", Steel Compos. Struct., 14(5), 511-521. crossref(new window)

11.
Bayat, M. and Abdollahzadeh, G. (2011a), "On the effect of the near field records on the steel braced frames equipped with energy dissipating devices", Latin Am. J. Solid. Struct., 8(4), 429-443. crossref(new window)

12.
Bayat, M. and Abdollahzadeh, G. (2011b), "Analysis of the steel braced frames equipped with ADAS devices under the far field records", Latin Am. J. Solid. Struct., 8(2), 163-181. crossref(new window)

13.
Bayat, M., Bayat, M. and Pakar, I. (2014f), "Nonlinear vibration of an electrostatically actuated microbeam", Latin Am. J. Solid. Struct., 11(3), 534-544. crossref(new window)

14.
Bayat, M., Bayat, M. and Pakar, I. (2014a), "The analytic solution for parametrically excited oscillators of complex variable in nonlinear dynamic systems under harmonic loading", Steel Compos. Struct., 17(1), 123-131. crossref(new window)

15.
Bayat, M., Bayat, M. and Pakar, I. (2014c), "Forced nonlinear vibration by means of two approximate analytical solutions", Struct. Eng. Mech., 50(6), 853-862. crossref(new window)

16.
Bayat, M., Bayat, M. and Pakar, I. (2014g), "Accurate analytical solutions for nonlinear oscillators with discontinuous", Struct. Eng. Mech., 51(2), 349-360. crossref(new window)

17.
Bayat, M., Pakar, I. and Bayat, M. (2013b), "On the large amplitude free vibrations of axially loaded Euler- Bernoulli beams", Steel Compos. Struct., 14(1), 73-83. crossref(new window)

18.
Bayat, M., Pakar, I. and Bayat, M. (2014b), "An accurate novel method for solving nonlinear mechanical systems", Struct. Eng. Mech., 51(3), 519-530. crossref(new window)

19.
Bayat, M., Pakar, I. and Emadi, A. (2013a), "Vibration of electrostatically actuated microbeam by means of homotopy perturbation method", Struct. Eng. Mech., 48(6), 823-831. crossref(new window)

20.
Bor-Lih, K. and Cheng-Ying, L. (2009), "Application of the differential transformation method to the solution of a damped system with high nonlinearity", Nonlin. Anal., 70(4), 1732-1737. crossref(new window)

21.
Cunedioglu ,Y. and Beylergil, B. (2014), "Free vibration analysis of laminated composite beam under room and high temperatures", Struct. Eng. Mech., 51(1), 111-130. crossref(new window)

22.
Cveticanin, L. (2012), "A review on dynamics of mass variable systems", J. Serbian Soc. Comput. Mech., 6(1), 56-74.

23.
Cveticanin, L. (2015), "A solution procedure based on the Ateb function for a two-degree-of-freedom oscillator", J. Sound Vib., 346, 298-313. crossref(new window)

24.
Dehghan, M. and Tatari, M. (2008), "Identifying an unknown function in a parabolic equation with over specified data via He's variational iteration method", Chaos, Soliton. Fract., 36(1), 157-166. crossref(new window)

25.
Evakin, A.Yu. and Kalamkarov, A. (2001), "Analysis of large deflection equilibrium state of composite shells of revolution. Part 1. General model and singular perturbation analysis", Int. J. Solid. Struct., 38(50- 51), 8961-8974. crossref(new window)

26.
Filippov, S.B. (1999), Theory of conjugated and reinforced shells, St. Petersburg state university. (in Russian)

27.
Filobello-Nino, U.H., Vazquez-Leal, B., Benhammouda, A., Perez-Sesma, V., Jimenez-Fernandez, J., Cervantes-Perez, A., Sarmiento-Reyes, J., Huerta-Chua, L., Morales-Mendoza and M., Gonzalez-Lee (2015), "Analytical solutions for systems of singular partial differential-algebraic equations", Discrete Dyn. Nat. Soc., Article ID 752523, 9 pages.

28.
Grigolyuk, E.I. and Kabanov, V.V. (1987), Stability of shells, Nauka, Moscow. (in Russian)

29.
Han, S. (1965), "On the free vibration of a beams on a nonlinear elastic foundation", Trans. ASME J. Appl. Mech., 32(2), 445-447. crossref(new window)

30.
He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos, Solitons Fract., 34(5), 1430-1439. crossref(new window)

31.
He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillations", Mech. Res. Commun., 29(2-3), 107-111. crossref(new window)

32.
He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A, 374(23), 2312-2314. crossref(new window)

33.
He, J.H. (2008), "An improved amplitude-frequency formulation for nonlinear oscillators", Int. J. Nonlin. Sci. Numer. Simul., 9(2), 211-212.

34.
Jamshidi, N. and Ganji, D.D. (2010), "Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire", Curr. Appl. Phys., 10(2), 484-486. crossref(new window)

35.
Mehdipour, I., Ganji, D.D. and Mozaffari, M. (2010), "Application of the energy balance method to nonlinear vibrating equations", Curr. Appl. Phys., 10(1), 104-112. crossref(new window)

36.
Nayfeh.A.H. (1973), Perturbation methods, volume 6, Wiley Online Library.

37.
Odibat, Z., Momani, S. and Suat Erturk, V. (2008), "Generalized differential transform method: application to differential equations of fractional order", Appl. Math. Comput., 197(2), 467-477.

38.
Pakar, I. and Bayat, M. (2013a), "Vibration analysis of high nonlinear oscillators using accurate approximate methods", Struct. Eng. Mech., 46(1), 137-151. crossref(new window)

39.
Pakar, I. and Bayat, M. (2013b), "An analytical study of nonlinear vibrations of buckled Euler Bernoulli beams", Acta Physica Polonica A, 123(1), 48-52. crossref(new window)

40.
Pakar, I., Bayat, M. and Bayat, M. (2011), "Analytical evaluation of the nonlinear vibration of a solid circular sector object", Int. J. Phys. Sci., 6(30), 6861-6866.

41.
Pakar, I., Bayat, M. and Bayat, M. (2014a), "Nonlinear vibration of thin circular sector cylinder: An analytical approach", Steel Compos. Struct., 17(1), 133-143. crossref(new window)

42.
Pakar, I., Bayat, M. and Bayat, M. (2014b), "Accurate periodic solution for nonlinear vibration of thick circular sector slab", Steel Compos. Struct., 16(5), 521-531. crossref(new window)

43.
Radomirovic, D. and Kovacic, I. (2015), "An equivalent spring for nonlinear springs in series", Eur. J. Phys., 36(5), 055004. crossref(new window)

44.
Rajasekaran, S. (2013), "Free vibration of tapered arches made of axially functionally graded materials", Struct. Eng. Mech., 45(4), 569-594. crossref(new window)

45.
Shahidi, M., Bayat, M., Pakar, I. and Abdollahzadeh, G.R. (2011), "Solution of free non-linear vibration of beams", Int. J. Phys. Sci., 6(7), 1628-1634.

46.
Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11), 2131-2133. crossref(new window)

47.
Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108. crossref(new window)

48.
Xu, L. (2010), "Application of Hamiltonian approach to an oscillation of a mass attached to a stretched elastic wire", Comput. Math. Appl., 15(5), 901-906.

49.
Xu, Nan and Zhang, A. (2009), "Variational approachnext term to analyzing catalytic reactions in short monoliths", Comput. Math. Appl., 58(11-12), 2460-2463. crossref(new window)

50.
Xu, R., Li, D.-X., Jiang, J.-P. and Liu, W. (2015), "Nonlinear vibration analysis of membrane SAR antenna structure adopting a vector form intrinsic finite element", J. Mech., 31(3), 269-277. crossref(new window)

51.
Zeng, D.Q. and Lee, Y.Y. (2009), "Analysis of strongly nonlinear oscillator using the max-min approach", Int. J. Nonlin. Sci. Numer. Simul., 10(10), 1361-1368.

52.
Zhifeng, L., Yunyao, Y., Feng, W., Yongsheng, Z. and Ligang, C. (2013), "Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam", Struct. Eng. Mech., 48(5): 697-709. crossref(new window)