On double-peak probability density functions of a Duffing oscillator under narrow-band random excitations

Hai Wu Rong; Xiang Dong Wang; Wei Xu; Guang Meng; Tong Fang

doi:10.7498/aps.54.2557

On double-peak probability density functions of a Duffing oscillator under narrow-band random excitations

Hai Wu Rong, Xiang Dong Wang, Wei Xu, Guang Meng, Tong Fang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The principal resonance of Duffing oscillator under the narrow-band random external excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The one-peak probability density function of each of the two stable stationary solutions is then calculated by perturbation analysis in the resonant case. These two functions are combined by using the probability of realization of the two stable stationary solutions to calculate the double-peak probability density function approximately. Theoretical analyses are verified by numerical results.

Original language	English
Pages (from-to)	2557-2561
Number of pages	5
Journal	Wuli Xuebao/Acta Physica Sinica
Volume	54
Issue number	6
DOIs	https://doi.org/10.7498/aps.54.2557
State	Published - Jun 2005

Keywords

Double peak probability density
Duffing oscillator
Linearization method
Multiple scale method

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10.7498/aps.54.2557

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abstract = "The principal resonance of Duffing oscillator under the narrow-band random external excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The one-peak probability density function of each of the two stable stationary solutions is then calculated by perturbation analysis in the resonant case. These two functions are combined by using the probability of realization of the two stable stationary solutions to calculate the double-peak probability density function approximately. Theoretical analyses are verified by numerical results.",

keywords = "Double peak probability density, Duffing oscillator, Linearization method, Multiple scale method",

author = "Rong, {Hai Wu} and Wang, {Xiang Dong} and Wei Xu and Guang Meng and Tong Fang",

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AU - Rong, Hai Wu

AU - Wang, Xiang Dong

AU - Xu, Wei

AU - Meng, Guang

AU - Fang, Tong

PY - 2005/6

Y1 - 2005/6

N2 - The principal resonance of Duffing oscillator under the narrow-band random external excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The one-peak probability density function of each of the two stable stationary solutions is then calculated by perturbation analysis in the resonant case. These two functions are combined by using the probability of realization of the two stable stationary solutions to calculate the double-peak probability density function approximately. Theoretical analyses are verified by numerical results.

AB - The principal resonance of Duffing oscillator under the narrow-band random external excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The one-peak probability density function of each of the two stable stationary solutions is then calculated by perturbation analysis in the resonant case. These two functions are combined by using the probability of realization of the two stable stationary solutions to calculate the double-peak probability density function approximately. Theoretical analyses are verified by numerical results.

KW - Double peak probability density

KW - Duffing oscillator

KW - Linearization method

KW - Multiple scale method

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DO - 10.7498/aps.54.2557

M3 - 文章

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JO - Wuli Xuebao/Acta Physica Sinica

JF - Wuli Xuebao/Acta Physica Sinica

IS - 6

ER -

On double-peak probability density functions of a Duffing oscillator under narrow-band random excitations

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Keywords

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