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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Volume 62, Issue 1, Pages 78–87
DOI: https://doi.org/10.15372/PMTF20210109
(Mi pmtf210)
 

This article is cited in 2 scientific papers (total in 2 papers)

Approximate analytical solutions to nonlinear damped oscillatory systems using a modified algebraic method

M. Mohammadian

Department of Mechanical Engineering, Gorgan Branch, Islamic Azad University, Gorgan, Iran
Abstract: In the current paper, a modified algebraic method (MAGM) is proposed as an effective semi-analytical technique for solving nonlinear damped oscillatory systems. A polynomial is supposed as the trial solution, and its unknown coefficients are easily determined through the algebraic method (AGM). In order to improve the solution, the Laplace transformation is applied to the series solution, and then the Padé approximants of the resultant equation are constructed. Finally, the inverse Laplace transformation is adopted to obtain a periodic solution for the nonlinear problem under consideration. The proposed method is then applied for obtaining approximate analytical solutions of a damped rotatory oscillator as well as nonlinear vibrations of a flexible beam excited by an axial force. The results are compared with those obtained by the fourth-order Runge–Kutta method, and good agreement is observed.
Keywords: algebraic method, nonlinear damped oscillator, nonlinear damping ratio, Runge–Kutta method.
Received: 11.02.2020
Revised: 22.04.2020
Accepted: 27.04.2020
English version:
Journal of Applied Mechanics and Technical Physics, 2021, Volume 62, Issue 1, Pages 70–78
DOI: https://doi.org/10.1134/S0021894421010090
Bibliographic databases:
Document Type: Article
UDC: 534.16
Language: Russian
Citation: M. Mohammadian, “Approximate analytical solutions to nonlinear damped oscillatory systems using a modified algebraic method”, Prikl. Mekh. Tekh. Fiz., 62:1 (2021), 78–87; J. Appl. Mech. Tech. Phys., 62:1 (2021), 70–78
Citation in format AMSBIB
\Bibitem{Moh21}
\by M.~Mohammadian
\paper Approximate analytical solutions to nonlinear damped oscillatory systems using a modified algebraic method
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2021
\vol 62
\issue 1
\pages 78--87
\mathnet{http://mi.mathnet.ru/pmtf210}
\crossref{https://doi.org/10.15372/PMTF20210109}
\elib{https://elibrary.ru/item.asp?id=44746886}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2021
\vol 62
\issue 1
\pages 70--78
\crossref{https://doi.org/10.1134/S0021894421010090}
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