Approximate solutionsof Damped Nonlinear Vibrating System with Varying Coefficients under Some Conditions
Applied and Computational Mathematics
Volume 1, Issue 1, December 2012, Pages: 1-5
Received: Dec. 30, 2012; Published: Dec. 30, 2012
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Authors
Pinakee Dey, Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh.
Babul Hossain, Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh.
Musa Miah, Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh.
Mohammad Mokaddes Ali, Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh.
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Abstract
Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended to certain damped-oscillatory nonlinear systems with varying coefficients. The solution obtained for different initial conditions for a second order nonlinear system show a good coincidence with those obtained by numerical method. The method is illustrated by an example.
Keywords
Nonlinear System, Varying Coefficient, Unperturbed Equation, Damped Oscillatory System
To cite this article
Pinakee Dey, Babul Hossain, Musa Miah, Mohammad Mokaddes Ali, Approximate solutionsof Damped Nonlinear Vibrating System with Varying Coefficients under Some Conditions, Applied and Computational Mathematics. Vol. 1, No. 1, 2012, pp. 1-5. doi: 10.11648/j.acm.20120101.11
References
[1]
N.N, Krylov and N.N., Bogoliubov, Introduction to Nonlinear Mechanics. Princeton University Press, New Jersey, 1947.
[2]
N. N, Bogoliubov and Yu. Mitropolskii, Asymptotic Methods 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.
[4]
I. P. Popov, "A generalization of the Bogoliubov asymptotic method in the theory of nonlinear oscillations", Dokl.Akad. Nauk SSSR 111, 1956, 308-310 (in Russian).
[5]
G.,Bojadziev, and J. Edwards, "On Some Asymptotic Methods for Non-oscillatory and Oscillatory Processes", Nonlinear Vibration Problems, 20, 1981, pp69-79.
[6]
I.S.N. Murty, "A Unified Krylov-Bogoliubov Method for Second Order Nonlinear Systems", Int. J. nonlinear Mech., 6, 1971, pp45-53.
[7]
M.,Shamsul Alam, "Unified Krylov-Bogoliubov-Mitropolskii Method for Solving n-th Order Nonlinear System with Slowly Varying Coefficients", Journal of Sound and Vibration, 256, 2003, pp987-1002.
[8]
Hung Cheng and Tai Tsun Wu, "An Aging Spring, Studies in Applied Mathematics", 49, 1970, pp183-185.
[9]
K.C, Roy, M. Shamsul Alam, "Effects of Higher Approximation of Krylov- Bogoliubov-Mitropolskii Solution and Matched Asymptotic Solution of a Differential System with Slowly Varying Coefficients and Damping Near to a Turning Point", Vietnam Journal of Mechanics, VAST, 26, 2004, pp182-192.
[10]
Pinakee Dey., Harun or Rashid, M. Abul Kalam Azad and M S Uddin, "Approximate Solution of Second Order Time Dependent Nonlinear Vibrating Systems with Slowly Varying Coefficients", Bull. Cal. Math. Soc, 103, (5), 2011, pp371-38.
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