Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems
Pure and Applied Mathematics Journal
Volume 2, Issue 2, April 2013, Pages: 101-105
Received: May 2, 2013; Published: May 20, 2013
Views 2685      Downloads 77
Author
Pinakee Dey, Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh
Article Tools
PDF
Follow on us
Abstract
Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and applied to certain over-damped nonlinear system in which the linear equation has two almost equal roots. The method is illustrated by an example.
Keywords
Nonlinear System, Unperturbed Equation, Over-Damped Oscillatory System, Equal Roots
To cite this article
Pinakee Dey, Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems, Pure and Applied Mathematics Journal. Vol. 2, No. 2, 2013, pp. 101-105. doi: 10.11648/j.pamj.20130202.18
References
[1]
N.N, Krylov and N.N., Bogoliubov, Introduction to Nonli-near Mechanics. Princeton University Press, New Jersey, 1947.
[2]
N. N, Bogoliubov and Yu. Mitropolskii, Asymptotic Me-thods in the Theory of nonlinear Oscillations, Gordan and Breach, New York, 1961.
[3]
Yu.,Mitropolskii, "Problems on Asymptotic Methods of Non-stationary Oscillations" (in Russian), Izdat, Nauka, Moscow, 1964.P. Popov, "A generalization of the Bogoli-ubov asymptotic method in the theory of nonlinear oscilla-tions", Dokl.Akad. Nauk SSSR 111, 1956, 308-310 (in Russian).
[4]
S. N. Murty, B. L. Deekshatulu and G. Krisna, "General asymptotic method of Krylov-Bogoliubov for over-damped nonlinear system", J. Frank Inst. 288 (1969), 49-46.
[5]
M.,Shamsul Alam, "A unified Krylov-Bogoliubov-Mitropolskii method for solving nth order nonlinear sys-tems", Journal of the Franklin Institute 339, 239-248, 2002.
[6]
M.,Shamsul Alam., "Asymptotic methods for second-order over-damped and critically damped nonlinear system", Soochow J. Math, 27, 187-200, 2001 .
[7]
Pinakee Dey, M. Zulfikar Ali, M. Shamsul Alam, An Asymptotic Method for Time Dependent Non-linear Over-damped Systems, J. Bangladesh Academy of sciences., Vol. 31, pp. 103-108, 2007.
[8]
Pinakee Dey, Method of Solution to the Over-Damped Nonlinear Vibrating System with Slowly Varying Coeffi-cients under Some Conditions, J. Mech. Cont. & Math. Sci. Vol -8 No-1, July, 2013.
[9]
H. Nayfeh, Introduction to perturbation Techniques, J. Wiley, New York, 1981.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186