Study of Autonomous Conservative Oscillator Using an Improved Perturbation Method

Abstract

Purpose

In a recent article (Manimegalai et al. in Eur Phys J Plus 134:462, 2019), Aboodh transform based homotopy perturbation method (AT) has been found to produce approximate analytical solutions in a simple way but with better accuracy in comparison to those obtained from some of the established approximation methods (Mehdipour et al. in Curr Appl Phys 10:104, 2010; Nofal et al. in J Electromagn Anal Appl 5(10):388, 2013) for some physically relevant anharmonic oscillators such as autonomous conservative oscillator (ACO).

Method

In the present article, expansion of frequency (\(\omega\)) and an auxiliary parameter (h) are incorporated in the framework of the homotopy perturbation method (HPM) to improve the accuracy by retaining its simplicity.

Results and conclusions

Laplace transform is used to make the calculation simpler. This improved HPM (LH) is simple but provides highly accurate results for ACO in comparison to those obtained from AT. The error in the values of frequency and displacement calculated using the LH is found to be one or two order of magnitude less than those obtained from AT for the considered parameter sets.

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Correspondence to Tapas Sil.

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Zephania, C.F.S., Sil, T. Study of Autonomous Conservative Oscillator Using an Improved Perturbation Method. J. Vib. Eng. Technol. (2020). https://doi.org/10.1007/s42417-020-00233-2

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Keywords

  • Homotopy perturbation method
  • Nonlinear oscillator
  • Analytical approximation