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

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

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

戎海武^1,2, 徐伟³, 王向东¹, 孟光^1,2, 方同⁴

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

收稿日期:2000-09-06 修回日期:2001-08-20 出版日期:2002-03-18 发布日期:2002-03-18
基金资助:
the National Natural Science Foundation of China(10072049,19972054);the Natural Science Foundation of Guangdong(9744)

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

RONG Hai-wu^1,2, XU Wei³, WANG Xiang-dong¹, MENG Guang^1,2, FANG Tong⁴

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)

摘要/Abstract

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.

中图分类号:

O324

戎海武;徐伟;王向东;孟光;方同. 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.

RONG Hai-wu;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.

参考文献

[1] ZHU Wei-qiu.Random Vibration[M].Beijing:Science Press,1992.(in Chinese)
[2] Stratonovitch R L, Romanovskii Y M. Parametric effect of a random force on linear and nonlinear oscillatory systems[A]. In: P T Kuznetsov, R L Stratonovitch, V I Tikhonov,Eds. Nonlinear Translations of Stochastic Process[C]. Oxford: Pegramon,1996.
[3] Dimentberg M F, Isikov N E, Model R. Vibration of a system with cubic-non-linear damping and simultaneous periodic and random parametric excitation[J]. Mechanics of Solids,1981,16(1):19-21.
[4] Namachchivaya N S. Almost sure stability of dynamical systems under combined harmonic and stochastic excitations[J]. Journal of Sound and Vibration,1991,151(1):77-91.
[5] Ariaratnam S T, Tam D S F. Parametric random excitation of a damped Mathieu oscillator[J]. ZAngew Math Mech,1976,56(3):449-452.
[6] Dimentberg M F. Statistical Dynamics of Nonlinear and Time-Varying Systems[M]. New York: Wiley,1988.
[7] RONG Hai-wu, XU Wei, FANG Tong. Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation[J]. Journal of Sound and Vibration, 1998,210(4):483-515.
[8] Wedig W V. Invariant measures and Lipunov exponents for generalized parameter fluctuations[J]. Structural Safety,1990,8(1):13-25.
[9] Nayfeh A H. Introduction to Perturbation Techniques[M]. New York: Wiley,1981.
[10] Rajan S, Davies H G. Multiple time scaling of the response of a Duffing oscillator to narrow-band excitations[J]. Journal of Sound and Vibration,1988,123(3):497-506.
[11] Nayfeh A H, Serhan S J. Response statistics of nonlinear systems to combined deterministic and random excitations[J]. International Journal of Nonlinear Mechanics,1990,25(5):493-509.
[12] Oseledec V I. A multiplicative ergodic theorem, Liapunov characteristic numbers for dynamical systems[J]. Transaction of the Moscow Mathematical Society,1968,19(2):197-231.
[13] Wiggins S. Global Bifurcations and Chaos-Analysis Methods[M]. New York: Springer-Verlag.1990.

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

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

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