Authors:
M. Ali Akbar,DOI NO:
Keywords:
Abstract
In this article an analytical approximate solution has been investigated for obtaining the transient response of fourth order more critically damped nonlinear systems. The results obtained by the presented technique agree with the numerical result obtained by the fourth order Runge-Kutta method nicely. An example is solved to illustrate the method.Refference:
1) Akbar, M. A. Paul A. C. and Sattar M.A., An Asymptotic Method of Krylov-Bogoliubov for Fourth Order Over-damped Nonliner Systems, Gaint, J. angladesh Math. Soc., Vol. 22, pp. 83-96, 2002.
2) Akbar, M.A. Shamsul Alam M. and Sattar M.A., Asymptotic Method for Fourth Order Damped Nonlinear Systems, Ganit, J. Bangladesh Math. Soc. Vol. 23, pp. 41-49, 2003.
3) Akbar, M. A, Shamsul Alam M. and . Sttar M., A Simple Technique for Obtaining Certain Over-damped Solutions of an (………………………) Order Nonlinear Differential Equation, Soochow of Mathematics Vol. 31(2), pp. 291-299, 2005.
4) Bogoliubov, N. N. and Mitropolski Yu., Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordan and Breach, New York, 1961.
5) Emdadul Hoque, M., M. Takasaki, . Ishino and . Mizuon, Development of a Three Axis Active Vibration Isolator Using Zero-Power Control, IEEE/ASME Transactions on Mechatronics, 2(4), 462-470, 2006.
6) Krylov, N. . and Bogoliubov N. N., Introduction to Nonlinear Mechanics, Princeton University Press, New Jersey, 1947.
7) Mendelson, K. S., Perturbation Theory for Damped Nonlinear Oscillations, J. Math. Physics, Vol. 2, pp. 3413-3415, 1970.
8) Mizuon, T., T. Toumia and M. Takasaki, Vibration Isolation System Using Negative Stiffness, JSME International Journal, Series C, 46(3), 517-523, 2003.
9) Murty, I. S. N., Deekshatulu B. L. and Krishna G., On an Asymptotic Method of Krylov-Bogoliubov for Over-damped Nonlinear System, J. Frank. Inst., Vol. 288, pp. 49-65, 1969.
10) Murty, I. S. N., A Unified Krylov-Bogoliubov Method for Solving Second Order Nonlinear Systems, Int. J. Nonlinear Mech. Ol. 6, pp. 45-53, 1971.
11) Popov, I. P., A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russian) Dokl. Akad. SSR Vol. 3, pp. 308-310, 1956.
12) Rokibul, M. I, Akbar M. A. and Samsuzzoha ., “A New Technique for Third Order Critically Damped Non-linear Systems, “Journal of Applied Sciences Research, Vol. 4(6), pp. 695-706, 2008.
13) Rokibul M. I, Sharif ddin M., Akbar M. A, Azmol Huda M. and Hossain S. M. ., A New Technique for Fourth Order Critically Damped Nonlinear System with Some Conditions, Bull. Cal. Math. Soc., Vol. 100(5), pp. 501-514, 2008.
14) Sattar, M. A., An asymptotic Method for Second Order Critically Damped Nonlinear Equations, J. Frank. Inst., Vol. 321, pp. 109-113, 1986.
15) Shamsul Alam, M. and Sattar M. ., An Asymptotic Method for Third Order Critically Damped Nonlinear Equations, J. Mathematical and Physical Sciences, Vol. 30, pp. 291-298,1996.
16) Shamsul Alam, M., Asymptotic Methods for Second Order Over-damped and Critically Damped Nonlinear Systems, Soochow Journal of Math. Vol. 27, pp. 187-200, 2001.
17) Shamsul Alam, M. Bogoliubov’s Method for Third Order Critically Damped Nonlinear Systems, Soochow J. Math. Vol. 28, pp. 65-80, 2002.