Principal response of Van der Pol-Duffing oscillator under combined deterministic and random parametric excitation

Rong Hai-wu; Xu Wei; Wang Xiang-dong; Meng Guang; Fang Tong

doi:10.1007/BF02438337

Principal response of Van der Pol-Duffing oscillator under combined deterministic and random parametric excitation

Rong Hai-wu, Xu Wei, Wang Xiang-dong, Meng Guang, Fang Tong

School of Mathematics and Statistics

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

12 Scopus citations

Abstract

The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.

Original language	English
Pages (from-to)	299-310
Number of pages	12
Journal	Applied Mathematics and Mechanics (English Edition)
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/BF02438337
State	Published - Mar 2002

Keywords

Largest Lyapunov exponent
Multiple scale method
Principal resonance
Steady state probability density function
Van Der Pol-Duffing oscillator

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10.1007/BF02438337

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title = "Principal response of Van der Pol-Duffing oscillator under combined deterministic and random parametric excitation",

abstract = "The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.",

keywords = "Largest Lyapunov exponent, Multiple scale method, Principal resonance, Steady state probability density function, Van Der Pol-Duffing oscillator",

author = "Rong Hai-wu and Xu Wei and Wang Xiang-dong and Meng Guang and Fang Tong",

year = "2002",

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doi = "10.1007/BF02438337",

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AU - Hai-wu, Rong

AU - Wei, Xu

AU - Xiang-dong, Wang

AU - Guang, Meng

AU - Tong, Fang

PY - 2002/3

Y1 - 2002/3

N2 - The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.

AB - The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.

KW - Largest Lyapunov exponent

KW - Multiple scale method

KW - Principal resonance

KW - Steady state probability density function

KW - Van Der Pol-Duffing oscillator

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U2 - 10.1007/BF02438337

DO - 10.1007/BF02438337

M3 - 文章

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VL - 23

SP - 299

EP - 310

JO - Applied Mathematics and Mechanics (English Edition)

JF - Applied Mathematics and Mechanics (English Edition)

IS - 3

ER -

Principal response of Van der Pol-Duffing oscillator under combined deterministic and random parametric excitation

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Keywords

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