RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (7): 817-825.

RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION

戎海武^1,2, 王向东¹, 孟光², 徐伟³, 方同³

1. Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P.R.China;
2. The State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, Shanghai 200030, P.R.China;
3. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

收稿日期:2000-08-30 修回日期:2002-12-01 出版日期:2003-07-18 发布日期:2003-07-18
通讯作者: ZHANG Shi-sheng and LI Li
基金资助:
the National Natural Science Foundation of China (10072049, 19972054);the Natural Science Foundation of Guangdong Province (000017);the Open Fund of the State Key Labora-tory of Vibration, Shock and Noise of Shanghai Jiaotong University (VSN-2002-04)

RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION

RONG Hai-wu^1,2, WANG Xiang-dong¹, MENG Guang², XU Wei³, FANG Tong ³

1. Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P.R.China;
2. The State Key Laboratory of Vibration, Shock 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:2000-08-30 Revised:2002-12-01 Online:2003-07-18 Published:2003-07-18
Supported by:
the National Natural Science Foundation of China (10072049, 19972054);the Natural Science Foundation of Guangdong Province (000017);the Open Fund of the State Key Labora-tory of Vibration, Shock and Noise of Shanghai Jiaotong University (VSN-2002-04)

摘要/Abstract

摘要： The principal resonance of Duffing oscillator to narrow-band random parametric excitation was 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 by means of qualitative analyses. The effects of damping, detuning, bandwidth and magnitudes of deterministic and random excitations were analyzed. The theoretical analyses were verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions.

Abstract: The principal resonance of Duffing oscillator to narrow-band random parametric excitation was 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 by means of qualitative analyses. The effects of damping, detuning, bandwidth and magnitudes of deterministic and random excitations were analyzed. The theoretical analyses were verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions.

中图分类号:

O324

戎海武;王向东;孟光;徐伟;方同. RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(7): 817-825.

RONG Hai-wu;WANG Xiang-dong;MENG Guang;XU Wei;FANG Tong . RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(7): 817-825.

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RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION

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