Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation

RONG Hai-wu; XU Wei; WANG Xiang-dang; MENG Guang; FANG TONG

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(3): 273-282

RONG Hai-wu, XU Wei, WANG Xiang-dang, MENG Guang, FANG TONG. Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation[J]. Applied Mathematics and Mechanics, 2002, 23(3): 273-282.

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Principal Response of Van der Pol-Duffing Oscillator Under Combined Deterministic and Random Parametric Exciation

1.
Foshan Institute of Science and Technology, Foshan, Guangdong 528000, P R China;
2.
State Key Laboratry of Vibration, Shoch and Noise, Shanghai Jiaotong University, Shanghai 200030, P R China;
3.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P R China

Received Date: 2000-09-06
Rev Recd Date: 2001-08-20
Publish Date: 2002-03-15

Abstract

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.
- principal resonance,
- Van der Pol-Duffing oscillator,
- multiple scate method,
- largest Liapunov exponent,
- steady state probebility density function

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References(13)

References

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