JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Nonlinear vibration of conservative oscillator`s using analytical approaches
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Nonlinear vibration of conservative oscillator`s using analytical approaches
Bayat, Mahmoud; Pakar, Iman; Bayat, Mahdi;
 Abstract
In this paper, a new analytical approach has been presented for solving nonlinear conservative oscillators. Variational approach leads us to high accurate solution with only one iteration. Two different high nonlinear examples are also presented to show the application and accuracy of the presented approach. The results are compared with numerical solution using runge-kutta algorithm in different figures and tables. It has been shown that the variatioanl approach doesn`t need any small perturbation and is accurate for nonlinear conservative equations.
 Keywords
analytical methods;nonlinear vibrations;numerical solution;
 Language
English
 Cited by
1.
Effect of granulated rubber on shear strength of fine-grained sand, Journal of Rock Mechanics and Geotechnical Engineering, 2017, 9, 5, 936  crossref(new windwow)
 References
1.
Bayat, M. and Pakar, I, (2011b), "Application of he's energy balance method for nonlinear vibration of thin circular sector cylinder", Int. J. Phy. Sci., 6(23), 5564-5570.

2.
Bayat, M. and Pakar, I. (2011a), "Nonlinear free vibration analysis of tapered beams by Hamiltonian approach", J. Vibroeng., 13(4), 654-661.

3.
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)

4.
Bayat, M. and Pakar, I. (2013b), "Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses", Earthq. Eng. Eng. Vib., 12(3), 411-420. crossref(new window)

5.
Bayat, M. and Pakar, I. (2013c), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52. crossref(new window)

6.
Bayat, M. and Pakar, I. (2015b), "Mathematical solution for nonlinear vibration equations using variational approach", Smart Struct. Syst., 15(5), 1311-1327. crossref(new window)

7.
Bayat, M., Bayat, M. and Pakar, I. (2014c), "Nonlinear vibration of an electrostatically actuated microbeam", Latin Am. J. Solid. Struct., 11(3), 534-544. crossref(new window)

8.
Bayat, M., Bayat, M. and Pakar, I. (2014d), "Forced nonlinear vibration by means of two approximate analytical solutions", Struct. Eng. Mech., 50(6), 853-862. crossref(new window)

9.
Bayat, M., Bayat, M. and Pakar, I. (2015a), "Analytical study of Nonlinear vibration of oscillators with damping", Earthq. Struct., 9(1), 221-232. crossref(new window)

10.
Bayat, M., Bayat, M. and Pakar, I. (2015c), "Analytical study of nonlinear vibration of oscillators with damping", Earthq. Struct., 9(1), 221-232. crossref(new window)

11.
Bayat, M., Pakar, I. and Bayat, M. (2013a), "Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell", Steel Compos. Struct., 14(5), 511-521. crossref(new window)

12.
Bayat, M., Pakar, I. and Bayat, M. (2014e), "Study of complex nonlinear vibrations by means of accurate analytical approach", Steel Compos. Struct., 17(5), 721-734. crossref(new window)

13.
Bayat, M., Pakar, I. and Cveticanin, L. (2014a), "Nonlinear free vibration of systems with inertia and static type cubic nonlinearities: an analytical approach", Mech. Machine Theory, 77, 50-58. crossref(new window)

14.
Bayat, M., Pakar, I. and Cveticanin, L. (2014b), "Nonlinear vibration of stringer shell by means of extended Hamiltonian approach", Arch. Appl. Mech., 84(1),43-50. crossref(new window)

15.
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.

16.
Bayat, M., Pakar, I. and Shahidi, M. (2011c), "Analysis of nonlinear vibration of coupled systems with cubic nonlinearity", Mechanika, 17(6), 620-629.

17.
Cordero, A., Hueso, J.L., Martinez, E. and Torregrosa, J.R. (2010), "Iterative methods for use with nonlinear discrete algebraic models", Math. Comput. Model., 52(7-8), 1251-1257. crossref(new window)

18.
Cveticanin, L. (2012), "A review on dynamics of mass variable systems", J. Serb. Soc. Comput. Mech., 6(1), 56-73.

19.
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)

20.
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 Solit. Fract., 36(1), 157-166. crossref(new window)

21.
Geng, L. and Cai, X.C. (2007), "He's frequency formulation for nonlinear oscillators", Eur. J. Phys., 28, 923-931. crossref(new window)

22.
He, J.H. (2004), "Solution of nonlinear equations by an ancient Chinese algorithm", Appl. Math. Comput., 151, 293-297.

23.
He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos Solit. Fract., 34(5), 1430-1439. crossref(new window)

24.
He, J.H. (2008), "An improved amplitude-frequency formulation for nonlinear oscillators", Int. J. Nonlin. Sci. Numer. Simul., 9(2), 211-212.

25.
He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A, 374(23), 2312-2314. crossref(new window)

26.
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, 484-486. crossref(new window)

27.
Kuo, B.L. and Lo, C.Y. (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)

28.
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)

29.
Odibat, Z., Momani, S. and Suat Erturk, V. (2008), "Generalized differential transform method: application to differential equations of fractional order", Appl. Math. Comput., 197, 467-477.

30.
Pakar, I. and Bayat, M. (2011a), "Analytical solution for strongly nonlinear oscillation systems using energy balance method", Int. J. Phys. Sci., 6(22), 5166-5170.

31.
Pakar, I. and Bayat, M. (2012b), "Analytical study on the non-linear vibration of Euler-Bernoulli beams", J. Vibroeng., 14(1), 216-224.

32.
Pakar, I. and Bayat, M. (2013a), "An analytical study of nonlinear vibrations of buckled Euler-Bernoulli beams", Acta Physica Polonica A, 123(1), 48-52. crossref(new window)

33.
Pakar, I. and Bayat, M. (2013b), "Vibration analysis of high nonlinear oscillators using accurate approximate methods", Struct. Eng. Mech., 46(1), 137-151. crossref(new window)

34.
Pakar, I., Bayat, M. and Bayat, M. (2012a), "On the approximate analytical solution for parametrically excited nonlinear oscillators", J. Vibroeng., 14(1), 423-429.

35.
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)

36.
Suna, W.P., Wua, B.S. and Lim, C.W. (2007), "Approximate analytical solutions for oscillation of a mass attached to a stretched elastic wire", J. Sound Vib., 300(5-6), 1042-1047. crossref(new window)

37.
Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108. crossref(new window)

38.
Xu, L. (2010), "Application of Hamiltonian approach to an oscillation of a mass attached to a stretched elastic wire", Math. Comput. Appl., 15(5), 901-906.

39.
Xu, N. and Zhang, A. (2009), "Variational approach next term to analyzing catalytic reactions in short monoliths", Comput. Math. Appl., 58(11-12), 2460-2463. crossref(new window)

40.
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.