Browse > Article
http://dx.doi.org/10.12989/scs.2014.17.1.133

Nonlinear vibration of thin circular sector cylinder: An analytical approach  

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 (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University)
Publication Information
Steel and Composite Structures / v.17, no.1, 2014 , pp. 133-143 More about this Journal
Abstract
In this paper, we try to prepare an accurate analytical solution for solving nonlinear vibration of thin circular sector cylinder. A new approximate solution called variational approach is presented and correctly applied to the governing equation of thin circular sector cylinder. The effect of important parameters on the response of the problem is considered. Some comparisons have been presented between the numerical solution and the present approach. The results show an excellent agreement between these methods. It has been illustrated that the variational approach can be a useful method to solve nonlinear problems by considering the effects of important parameters.
Keywords
thin circular sector cylinder; nonlinear vibration; variational approach;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Pakar, I. and Bayat, M. (2011), "Analytical solution for strongly nonlinear oscillation systems using energy balance method", Int. J. Phy. Sci., 6(22), 5166-5170.
2 Alicia, C., 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
3 Bayat, M. and Pakar, I. (2011a), "Nonlinear free vibration analysis of tapered beams by Hamiltonian Approach", J. Vibroeng., 13(4), 654-661.
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. and Pakar, I. (2013b), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52.   DOI
8 Bayat, M., Pakar, I. and Shahidi, M. (2011), "Analysis of nonlinear vibration of coupled systems with cubic nonlinearity", Mechanika, 17(6), 620-629.
9 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 Am. J. Solid. Struct., 9(2), 145-234.
10 Pakar, I. and Bayat, M. (2012), "Analytical study on the non-linear vibration of Euler-Bernoulli beams", J. Vibroeng., 14(1), 216-224.
11 Pakar, I., Bayat, M. and Bayat, M. (2012), "On the approximate analytical solution for parametrically excited nonlinear oscillators", J. Vibroeng., 14(1), 423-429.
12 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
13 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
14 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
15 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
16 Wu, G. (2011), "Adomian decomposition method for non-smooth initial value problems", Math. Comput. Model., 54(9-10), 2104-2108.   DOI   ScienceOn
17 Xu, L. (2008), "Variational approach to solution of nonlinear dispersive K(m, n) equation", Chaos Solitons Fractals, 37(1), 137-143.   DOI   ScienceOn
18 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.
19 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.   DOI   ScienceOn
20 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
21 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
22 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 Solitons Fractals, 36(1), 157-166.   DOI   ScienceOn
23 He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillators", Mech. Res. Communications, 29(2), 107-111.   DOI   ScienceOn
24 He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos Solitons Fractals, 34(5), 1430-1439.   DOI   ScienceOn
25 He, J.H. (2008), "An improved amplitude-frequency formulation for nonlinear oscillators", Int. J. Nonlinear Sci. Numer. Simulation, 9(2), 211-212.
26 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
27 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
28 Odibat, Z., Momani, S. and Erturk, V.S. (2008), "Generalized differential transform method: application to differential equations of fractional order", Appl. Math. Comput., 197(2) , 467-477.   DOI   ScienceOn
29 Bayat, M., Pakar, I. and Cveticanin, L. (2014a), "Nonlinear free vibration of systems with inertia and static type cubic nonlinearities: An analytical approach", Mech. Mach. Theory, 77, 50-58.   DOI   ScienceOn
30 Xu, N. and Zhang, A. (2009), "Variational approachnext term to analyzing catalytic reactions in short monoliths", Comput. Math. Appl., 58(11-12), 2460-2463.   DOI   ScienceOn