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http://dx.doi.org/10.12989/eas.2017.13.2.131

Energy based approach for solving conservative nonlinear systems  

Bayat, M. (Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University)
Pakar, I. (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University)
Cao, M.S. (Department of Engineering Mechanics, Hohai University)
Publication Information
Earthquakes and Structures / v.13, no.2, 2017 , pp. 131-136 More about this Journal
Abstract
This paper concerns two new analytical approaches for solving high nonlinear vibration equations. Energy Balance method and Hamiltonian Approach are presented and successfully applied for nonlinear vibration equations. In these approaches, there is no need to use small parameters to solve and only with one iteration, high accurate results are reached. Numerical procedures are also presented to compare the results of analytical and numerical ones. It has been established that, the proposed approaches are in good agreement with numerical solutions.
Keywords
conservative systems; nonlinear vibration; Energy Balance method; Hamiltonian Approach;
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Times Cited By KSCI : 4  (Citation Analysis)
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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.   DOI
2 Bayat, M. and Pakar, I. (2015a), "Mathematical solution for nonlinear vibration equations using variational approach", Smart Struct. Syst., 15(5), 1311-1327.   DOI
3 Bayat, M., Bayat, M. and Pakar, I. (2015b), "Analytical study of nonlinear vibration of oscillators with damping", Earthq. Struct., 9(1), 221-232.   DOI
4 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.
5 Cai, X.C. and Liu, J.F. (2011), "Application of the modified frequency formulation to a nonlinear oscillator", Comput. Math. Appl., 61(8), 2237-2240.   DOI
6 Civalek, O. (2006), "Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation", J. Sound Vib., 294(4), 966-980.   DOI
7 Civalek, O. (2013), "Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches", Compos. Part B: Eng., 50, 171-179.   DOI
8 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.   DOI
9 He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A, 374(23), 2312-2314.   DOI
10 He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillators", Mech. Res. Commun., 29(2), 107-111.   DOI
11 Huseyin, K. and Lin, R. (1991), "An Intrinsic multiple- time-scale harmonic balance method for nonlinear vibration and bifurcation problems", Int. J. Nonlinear Mech., 26(5), 727-740.   DOI
12 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.   DOI
13 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., ASME, 50(4), 871-876.   DOI
14 Sedighi, H.M., Koochi, A., Daneshmand, F. and Abadyan, M. (2015), "Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow", Int. J. Non-Linear Mech., 77, 96-106.   DOI
15 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.   DOI
16 Pakar, I. and Bayat, M. (2015), "Nonlinear vibration of stringer shell: An analytical approach", Proc. Inst. Mech. Engineers, Part E: J. Process Mech. Eng., 229(1), 44-51.   DOI
17 Sedighi, H.M. and Bozorgmehri, A. (2016), "Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory", Acta Mechanica, 227(6), 1575-1591.   DOI
18 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.
19 Shaban, M., Ganji, D.D. and Alipour, A.A. (2010), "Nonlinear fluctuation, frequency and stability analyses in free vibration of circular sector oscillation systems", Curr. Appl. Phys., 10(5), 1267-1285.   DOI
20 Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11), 2131-2133.   DOI
21 Zeng, D.Q. and Lee, Y.Y. (2009), "Analysis of strongly nonlinear oscillator using the max-min approach", Int. J. Nonlinear Sci. Numer. Simulat., 10(10), 1361-1368.
22 Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108.   DOI