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Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems

Received: 2 May 2013     Published: 20 May 2013
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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.

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 2)
DOI 10.11648/j.pamj.20130202.18
Page(s) 101-105
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Nonlinear System, Unperturbed Equation, Over-Damped Oscillatory System, Equal Roots

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.
Cite This Article
  • APA Style

    Pinakee Dey. (2013). Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems. Pure and Applied Mathematics Journal, 2(2), 101-105. https://doi.org/10.11648/j.pamj.20130202.18

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    ACS Style

    Pinakee Dey. Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems. Pure Appl. Math. J. 2013, 2(2), 101-105. doi: 10.11648/j.pamj.20130202.18

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    AMA Style

    Pinakee Dey. Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems. Pure Appl Math J. 2013;2(2):101-105. doi: 10.11648/j.pamj.20130202.18

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  • @article{10.11648/j.pamj.20130202.18,
      author = {Pinakee Dey},
      title = {Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems},
      journal = {Pure and Applied Mathematics Journal},
      volume = {2},
      number = {2},
      pages = {101-105},
      doi = {10.11648/j.pamj.20130202.18},
      url = {https://doi.org/10.11648/j.pamj.20130202.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.18},
      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.},
     year = {2013}
    }
    

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Author Information
  • Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh

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