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http://dx.doi.org/10.12989/sem.2018.65.4.409

Nonlinear vibration of oscillatory systems using semi-analytical approach  

Bayat, Mahmoud (Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University)
Bayat, Mahdi (Department of Civil Engineering, Roudehen Branch, Islamic Azad University)
Pakar, Iman (Mashhad Branch, Islamic Azad University)
Publication Information
Structural Engineering and Mechanics / v.65, no.4, 2018 , pp. 409-413 More about this Journal
Abstract
In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.
Keywords
variational approach (VA); nonlinear oscillators; Runge-Kutta's algorithm;
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Times Cited By KSCI : 8  (Citation Analysis)
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1 Bayat, M., Bayat, M. and Pakar, I. (2015c), "Analytical study of nonlinear vibration of oscillators with damping", Earthq. Struct., 9(1), 221-232.   DOI
2 Bayat, M., Pakar, I. and Domaiirry, G. (2012), "Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: A review", Lat. Am. J. Sol. Struct., 9(2), 145-234.
3 Bayat, M., Pakar, I. and Bayat, M. (2016), "Nonlinear vibration of conservative oscillator's using analytical approaches", Struct. Eng. Mech., 59(4), 671-682.   DOI
4 Chen, G. (1987), "Applications of a generalized Galerkin's method to non-linear oscillations of two-degree-of-freedom systems", J. Sound Vibr., 119, 225-242.   DOI
5 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, M. and Gonzalez-Lee (2015), "Analytical solutions for systems of singular partial differential-algebraic equations", Discr. Dyn. Nat. Soc., Article ID 752523, 9.
6 Hashemi Kachapi, S.M. and Ganji, D.D. (2013), Dynamics and Vibrations: Progress in Nonlinear Analysis, Springer.
7 He, J.H. (1999), "Variational iteration method: A kind of nonlinear analytical technique: some examples", J. Non-Lin. Mech., 34(4), 699-708.   DOI
8 He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos Solit. Fract., 34(5), 1430-1439.   DOI
9 He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillations", Mech. Res. Commun., 29, 107-111.   DOI
10 Kaya, M.O. and Demirbag, S.A. (2013), "Application of parameter expansion method to the generalized nonlinear discontinuity equation", Chaos Solit. Fract., 42(4), 1967-1977.   DOI
11 Radomirovic, D. and Kovacic, I. (2015), "An equivalent spring for nonlinear springs in series", Eur. J. Phys., 36(5), 055004.   DOI
12 Mehdipou, 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.   DOI
13 Ozis, T. and Yildirim, A. (2017), "A note on He's homotopy perturbation method for van der pol oscillator with very strong nonlinearity", Chaos Solit. Fract., 34(3), 989-991.   DOI
14 Pakar, I. and Bayat, M. (2015), "Nonlinear vibration of stringer shell: An analytical approach", Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 229(1), 44-51.   DOI
15 He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A., 374, 2312-2314.   DOI
16 Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11), 2131-2133.   DOI
17 Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Modell., 54(9-10), 2104-2108.   DOI
18 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.   DOI
19 Lau, S.L., Cheung, Y.K. and Wu, S.Y. (1983), "Incremental harmonic balance method with multiple time scales for aperiodic vibration of nonlinear systems", J. Appl. Mech., 50(4), 871-876.   DOI
20 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.   DOI
21 Baki, O. and Safa, B.C. (2011), "The homotopy perturbation method for free vibration analysis of beam on elastic foundation'', Struct. Eng. Mech., 37(4) 415-425.   DOI
22 Bayat, M. and Pakar, I. (2017), "Accurate semi-analytical solutionfor nonlinear vibration of conservative mechanical problems", Struct. Eng. Mech., 61(5), 657-661.   DOI
23 Bayat, M., Bayat, M. and Pakar, I. (2015a), "Analytical study of nonlinear vibration of oscillators with damping", Earthq. Struct., 9(1), 221-232.   DOI
24 Bayat, M. and Pakar, I. (2015b), "Mathematical solution for nonlinear vibration equations using variational approach", Smart Struct. Syst., 15(5), 1311-1327.   DOI