Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators
| Autor: | Ji-Huan He, Andres Garcia, Dan-Ni Yu |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Acoustics and Ultrasonics
Mechanical Engineering lcsh:Control engineering systems. Automatic machinery (General) lcsh:QC221-246 Duffing equation 02 engineering and technology Building and Construction 01 natural sciences lcsh:TJ212-225 Nonlinear oscillators 020303 mechanical engineering & transports Geophysics Variational iteration method Development (topology) 0203 mechanical engineering Mechanics of Materials lcsh:Acoustics. Sound 0103 physical sciences Applied mathematics Homotopy perturbation method 010301 acoustics Civil and Structural Engineering Mathematics |
| Zdroj: | Journal of Low Frequency Noise, Vibration and Active Control, Vol 38 (2019) |
| ISSN: | 2048-4046 1461-3484 |
| DOI: | 10.1177/1461348418811028 |
| Popis: | A brief introduction to the development of the homotopy perturbation method is given, and the main milestones are elucidated with more than 90 references. This paper further improves the method by constructing a homotopy equation with one or more auxiliary parameters embedding in the linear term with a clear advantage in accelerating and controlling the approximation convergence speed. Moreover, a revision of a recent amplitude-period approximation formula is presented providing an answer to an open problem related to the optimal approximation along with a new universal formula. Duffing equation is used as an example to illustrate the solution process for the homotopy perturbation method, and only one or few iterations are needed in practical applications, making the method much attractive. From the side of amplitude-period formulation, the nonlinear pendulum, the Duffing equation and an oscillator with discontinuity are analyzed providing an asymptotic exact equivalence for bigger parameter values in the case of Duffing’s system. This mini review gives a tutorial guideline for practical applications of the homotopy perturbation method, the references are not exhaustive. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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