Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (3): 299-310.

• Articles • Previous Articles     Next Articles

PRINCIPAL RESPONSE OF VAN DER POL-DUFFING OSCILLATOR UNDER COMBINED DETERMINISTIC AND RANDOM PARAMETRIC EXCITATION

RONG Hai-wu1,2, XU Wei3, WANG Xiang-dong1, MENG Guang1,2, FANG Tong4   

  1. 1. Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P. R. China;
    2. State Key Laboratory 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;
    4. Center of Random Vibration, Northwestern Polytechnical University, Xi’an 710072, P. R. China
  • Received:2000-09-06 Revised:2001-08-20 Online:2002-03-18 Published:2002-03-18
  • Supported by:
    the National Natural Science Foundation of China(10072049,19972054);the Natural Science Foundation of Guangdong(9744)

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.

2010 MSC Number: 

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