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| PRINCIPAL RESPONSE OF VAN DER POL-DUFFING OSCILLATOR UNDER COMBINED DETERMINISTIC AND RANDOM PARAMETRIC EXCITATION | |
| 作者姓名： | 戎海武 徐伟 王向东 孟光 方同 |
| 作者单位： | 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 |
| 基金项目： | theNationalNaturalScienceFoundationofChina( 1 0 0 72 0 49，1 9972 0 54 )，theNaturalScienceFoundationofGuangdong( 9744 ) |
| 摘 要： | ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｙｏｆｒａｎｄｏｍｐａｒａｍｅｔｒｉｃｅｘｃｉｔｅｄｓｙｓｔｅｍｓａｒｅｍｏｒｅｉｍｐｏｒｔａｎｔｔｈａｎｔｈａｔｏｆｒａｎｄｏｍｅｘｔｅｒｎａｌｅｘｃｉｔｅｄｏｎｅｓ,ａｎｄａｒｅｔｈｅｏｒｅｔｉｃａｌｌｙｍｏｒｅｄｉｆｆｉｃｕｌｔｅｓｐｅｃｉａｌｌｙｗｈｅｎｔｈｅｅｘｃｉｔａｔｉｏｎｓａｒｅｎａｒｒｏｗ＿ｂａｎｄｒａｎｄｏｍｐｒｏｃｅｓｓｅｓ1].Ｉｎｔｈｅｃａｓｅｗｈｅｎｔｈｅｓｙｓｔｅｍｓａｒｅｅｘｃｉｔｅｄｂｙｃｏｍｂｉｎｅｄｄｅｔｅｒｍｉｎｉｓｔｉ… |
| 收稿时间： | 6 September 2000 |
Principal response of van der pol-duffing oscillator under combined deterministic and random parametric excitation |
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| Rong Hai-wu Associate Professor, Doctor,Xu Wei,Wang Xiang-dong,Meng Guang,Fang Tong.PRINCIPAL RESPONSE OF VAN DER POL-DUFFING OSCILLATOR UNDER COMBINED DETERMINISTIC AND RANDOM PARAMETRIC EXCITATION[J].Applied Mathematics and Mechanics(English Edition),2002,23(3):299-310. | |
| Authors: | Rong Hai-wu Associate Professor Doctor Xu Wei Wang Xiang-dong Meng Guang Fang Tong |
| Institution: | 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 |
| 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: | principal resonance Van der Pol-Duffing oscillator multiple scate method largest Lyapunov exponent steady state probability density function |
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