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Study of Autonomous Conservative Oscillator Using an Improved Perturbation Method
Journal of Vibration Engineering & Technologies ( IF 2.7 ) Pub Date : 2020-08-02 , DOI: 10.1007/s42417-020-00233-2
C. F. Sagar Zephania , Tapas Sil

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.



中文翻译:

改进摄动法研究自治保守振荡器。

目的

在最近的一篇文章中(Manimegalai等人在Eur Phys J Plus 134:462,2019中),发现基于Aboodh变换的同态微扰方法(AT)可以以简单的方式产生近似的解析解,但与之相比具有更高的准确性从某些已建立的近似方法(Mehdipour等人在Curr Appl Phys 10:104,2010; Nofal等人在J Electromagn Anal Appl 5(10):388,2013)中获得了一些与物理相关的非谐振荡器的信息,例如自主保守振荡器(ACO)。

方法

在本文中,将频率扩展(\(\ omega \))和一个辅助参数(h)合并到同伦摄动方法(HPM)的框架中,以通过保持其简单性来提高精度。

结果与结论

拉普拉斯变换用于简化计算。这种改进的HPM(LH)很简单,但是与从AT获得的结果相比,ACO可以提供高度准确的结果。发现使用LH计算的频率和位移值的误差比考虑参数集的AT误差小一个或两个数量级。

更新日期:2020-08-02
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