Browse > Article
http://dx.doi.org/10.12989/scs.2014.16.5.521

Accurate periodic solution for nonlinear vibration of thick circular sector slab  

Pakar, Iman (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University)
Bayat, Mahmoud (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University)
Bayat, Mahdi (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University)
Publication Information
Steel and Composite Structures / v.16, no.5, 2014 , pp. 521-531 More about this Journal
Abstract
In this paper we consider a periodic solution for nonlinear free vibration of conservative systems for thick circular sector slabs. In Energy Balance Method (EBM) contrary to the conventional methods, only one iteration leads to high accuracy of the solutions. The excellent agreement of the approximate frequencies and periodic solutions with the exact ones could be established. Some patterns are given to illustrate the effectiveness and convenience of the methodology. Comparing with numerical solutions shows that the energy balance method can converge to the numerical solutions very rapidly which are valid for a wide range of vibration amplitudes as indicated in this paper.
Keywords
thick circular sector cylinder; nonlinear vibration; energy balance method;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Cordero, A., Hueso, J.L., Martinez, E. and Torregros, J.R. (2010), "Iterative methods for use with nonlinear discrete algebraic models", Math. Comput. Model., 52(7-8), 1251-1257.   DOI   ScienceOn
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. (2013b), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52.   DOI
4 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.
5 Bayat, M. and Pakar, I. (2012), "Accurate analytical solution for nonlinear free vibration of beams", Struct. Eng. Mech., Int. J., 43(3), 337-347.   DOI   ScienceOn
6 Bayat, M. and Pakar, I. (2013a), "Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses", Earthq. Eng. Eng. Vib., 12(3), 411-420 .   DOI
7 Bayat, M., Pakar, I. and Shahidi, M. (2011), "Analysis of nonlinear vibration of coupled systems with cubic nonlinearity", Mechanika, 17(6), 620-629.
8 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", Latin American J. Solid. Struct., 9(2), 145-234.
9 Bayat, M., Pakar, I. and Bayat, M. (2013), "Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell", Steel Compos. Struct., Int. J., 14(5), 511-521.   DOI   ScienceOn
10 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. DOI: 10.1016/j.mechmachtheory.2014.02.009   DOI   ScienceOn
11 Bayat, M., Bayat, M. and Pakar, I. (2014c), "Nonlinear vibration of an electrostatically actuated microbeam", Latin Am. J. Solid. Struct., 11(3), 534-544.   DOI
12 Kuo, B.L. and Lo, C.Y. (2009), "Application of the differential transformation method to the solution of a damped system with high nonlinearity", Nonlinear Anal., 70(4), 1732-1737.   DOI   ScienceOn
13 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.   DOI   ScienceOn
14 He J.H. (2008), "An improved amplitude-frequency formulation for nonlinear oscillators", Int. J. Nonlinear Sci. Numer. Simul., 9(2), 211-212.
15 He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillators", Mech. Res. Comm., 29(2), 107-111.   DOI   ScienceOn
16 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.   DOI   ScienceOn
17 He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos Soliton. Fract., 34(5), 1430-1439.   DOI   ScienceOn
18 Mehdipour, I., Ganji, D.D. and Mozaffari, M. (2010), "Application of the energy balance method to nonlinear vibrating equations", Current Appl. Phys., 10(1), 104-112.   DOI   ScienceOn
19 Pakar, I. and Bayat, M. (2011), "Analytical solution for strongly nonlinear oscillation systems using energy balance method", Int. J. Phys. Sci., 6(22), 5166-5170.
20 Pakar, I. and Bayat, M. (2012), "Analytical study on the non-linear vibration of Euler-Bernoulli beams", J. Vibroeng., 14(1), 216-224.
21 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.   DOI
22 Pakar, I. and Bayat, M. (2013b), "Vibration analysis of high nonlinear oscillators using accurate approximate methods", Struct. Eng. Mech., Int. J., 46(1), 137-151.   DOI   ScienceOn
23 Xu, L. (2008), "Variational approach to solution of nonlinear dispersive K(m, n) equation", Chaos Soliton. Fract., 37(1), 137-143.   DOI   ScienceOn
24 Shaban, M., Ganji, D.D. and Alipour, A.A. (2010), "Nonlinear fluctuation, frequency and stability analyses in free vibration of circular sector oscillation systems", Current Appl. Phys., 10(5), 1267-1285.   DOI   ScienceOn
25 Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11), 2131-2133.   DOI   ScienceOn
26 Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108.   DOI   ScienceOn
27 Xu, L. and Zhang, N. (2009), "Variational approachnext term to analyzing catalytic reactions in short monoliths", Comput. Math. Appl., 58(11-12), 2460-2463.   DOI   ScienceOn
28 Zeng, D.Q. and Lee, Y.Y. (2009), "Analysis of strongly nonlinear oscillator using the max-min approach", Int. J. Nonlinear Sci. Numer. Simul., 10(10), 1361-1368.
29 Pakar, I., Bayat, M. and Bayat, M. (2012), "On the approximate analytical solution for parametrically excited nonlinear oscillators", J. Vibroeng., 14(1), 423-429.
30 Bayat, M., Pakar, I. and Cveticanin, L. (2014b), "Nonlinear vibration of stringer shell by means of extended Hamiltonian approach", Archive Appl. Mech., 84(1), 43-50.   DOI   ScienceOn