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Analytical solution of nonlinear differential equations two oscillators mechanism using Akbari–Ganji method

Saman Hosseinzadeh

Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

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Kh. Hosseinzadeh

Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

E-mail Address: [email protected]

Corresponding author.

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M. Rahai

Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

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, and

D. D. Ganji

https://orcid.org/0000-0002-4293-5993

Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0217984921504625Cited by:30 (Source: Crossref)

Abstract

In the last decade, many potent analytical methods have been utilized to find the approximate solution of nonlinear differential equations. Some of these methods are energy balance method (EBM), homotopy perturbation method (HPM), variational iteration method (VIM), amplitude frequency formulation (AFF), and max–min approach (MMA). Besides the methods mentioned above, the Akbari–Ganji method (AGM) is a highly efficient analytical method to solve a wide range of nonlinear equations, including heat transfer, mass transfer, and vibration problems. In this study, it was constructed the approximate analytic solution for movement of two mechanical oscillators by employing the AGM. In the derived analytical method, both oscillator motion equations and the sensitivity analysis of the frequency were included. The AGM was validated through comparison against Runge–Kutta fourth-order numerical method and an excellent agreement was achieved. Based on the results, the highest sensitivity of the oscillation frequency is related to the mass. As $α$ and $β$ increase, the slope of the system velocity and acceleration will increase.

Keywords:

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Vol. 35, No. 31

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History

Received 13 June 2021

Revised 21 July 2021

Accepted 22 July 2021

Published: 20 August 2021

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Analytical solution of nonlinear differential equations two oscillators mechanism using Akbari–Ganji method

Abstract

References

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Analytical solution of nonlinear differential equations two oscillators mechanism using Akbari–Ganji method

Abstract

References

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