Pure and Applied Mathematics Journal

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Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems

Received: 02 May 2013    Accepted:     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.

DOI 10.11648/j.pamj.20130202.18
Published in Pure and Applied Mathematics Journal (Volume 2, Issue 2, April 2013)
Page(s) 101-105
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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), 2024. 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.
Author Information
  • Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh

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  • 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://download.sciencepg.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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