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Modified Krylov-Bogoliubov-Mitropolskii method for solving damped nonlinear oscillators.

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Title: Modified Krylov-Bogoliubov-Mitropolskii method for solving damped nonlinear oscillators.
Authors: Islam, Md. Mohaiminul1 (AUTHOR), Alam, Md. Zahangir1 (AUTHOR), Hosen, Md. Alal1 (AUTHOR) alal_ruet@yahoo.com
Source: Noise & Vibration Worldwide. Mar2026, Vol. 57 Issue 3, p130-138. 9p.
Subjects: Nonlinear oscillators, Damping (Mechanics), Duffing equations, Perturbation theory, Inertia (Mechanics), Runge-Kutta formulas, Approximation theory
Abstract: In the recent past, a simplified solution was obtained by using a modified Krylov-Bogoliubov-Mitropolskii method for a cubic Duffing oscillator in the presence of a linear damped force. However, a similar solution is not always possible for another class of nonlinear oscillators where the inertia type force is involved in the nonlinear function along with the restoring forces and in the presence of linear damping. In this paper, an alternative modification of the Krylov-Bogoliubov-Mitropolskii method is introduced to overcome this limitation. The approximated solutions are achieved and comparison with the fourth-order Runge-Kutta method which are represented graphically. The comparison reveals excellent consistency between them. [ABSTRACT FROM AUTHOR]
Copyright of Noise & Vibration Worldwide is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Modified Krylov-Bogoliubov-Mitropolskii method for solving damped nonlinear oscillators.
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  Data: <searchLink fieldCode="AR" term="%22Islam%2C+Md%2E+Mohaiminul%22">Islam, Md. Mohaiminul</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Alam%2C+Md%2E+Zahangir%22">Alam, Md. Zahangir</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hosen%2C+Md%2E+Alal%22">Hosen, Md. Alal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> alal_ruet@yahoo.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Noise+%26+Vibration+Worldwide%22">Noise & Vibration Worldwide</searchLink>. Mar2026, Vol. 57 Issue 3, p130-138. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+oscillators%22">Nonlinear oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Damping+%28Mechanics%29%22">Damping (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Duffing+equations%22">Duffing equations</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Inertia+%28Mechanics%29%22">Inertia (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Runge-Kutta+formulas%22">Runge-Kutta formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink>
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  Label: Abstract
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  Data: In the recent past, a simplified solution was obtained by using a modified Krylov-Bogoliubov-Mitropolskii method for a cubic Duffing oscillator in the presence of a linear damped force. However, a similar solution is not always possible for another class of nonlinear oscillators where the inertia type force is involved in the nonlinear function along with the restoring forces and in the presence of linear damping. In this paper, an alternative modification of the Krylov-Bogoliubov-Mitropolskii method is introduced to overcome this limitation. The approximated solutions are achieved and comparison with the fourth-order Runge-Kutta method which are represented graphically. The comparison reveals excellent consistency between them. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Noise & Vibration Worldwide is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1177/09574565251391217
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 9
        StartPage: 130
    Subjects:
      – SubjectFull: Nonlinear oscillators
        Type: general
      – SubjectFull: Damping (Mechanics)
        Type: general
      – SubjectFull: Duffing equations
        Type: general
      – SubjectFull: Perturbation theory
        Type: general
      – SubjectFull: Inertia (Mechanics)
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      – SubjectFull: Runge-Kutta formulas
        Type: general
      – SubjectFull: Approximation theory
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      – TitleFull: Modified Krylov-Bogoliubov-Mitropolskii method for solving damped nonlinear oscillators.
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            NameFull: Islam, Md. Mohaiminul
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              M: 03
              Text: Mar2026
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              Y: 2026
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