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

作　　者：戎海武 徐伟 王向东 孟光 方同 

机构地区：[1]Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P R China,State Key Laboratory of Vibration, Shoch and Noise, Shanghai Jiaotong University, Shanghai 200030, P R China [2]Department of Applied Mathematics, Northwestern Polytechnical University,Xi'an 710072, P R China [3]Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P R China [4]Center of Random Vibration, Northwestern Polytechnical University,Xi'an 710072, P R China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2002年第3期299-310,共12页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina( 1 0 0 72 0 49;1 9972 0 54 ) ;theNaturalScienceFoundationofGuangdong( 9744 )

摘　　要：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.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.

关 键 词：principal resonance Van der Pol-Duffing oscillator multiple scate method largest Lyapunov exponent steady state probability density function 

分 类 号：O324[理学—一般力学与力学基础]