RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION

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

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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)

Abstract

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.

2010 MSC Number:

O324

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

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References

[1] Den Hartog J P. Mechanical Vibration,s [M]. Fourth edition. New York:McGraw-Hill, 1956.
[2] Lyon R H,Heckl M,Hazelgrove C B. Response of hard-spring oscillator to narrow-band excitation[J]. Journal of the Acoustical Society of America, 1961,33(4): 1404 - 1411.
[3] Richard K, Anand G V. Nonlinear resonance in strings under narrow band random excitation-part Ⅰ:planar response and stability[J]. Journal of Sound and Vibration, 1983,86(8):85 - 98.
[4] Davies H G, Nandall D. Phase plane for narrow band random excitation of a Duffing oscillator[J].Journal of Sound and Vibration, 1986,104 (2): 277 - 283.
[5] Iyengar R N. Response of nonlinear systems to narrow-band excitation[J]. Structural Safety, 1989,6(2): 177 - 185.
[6] Lennox W C, Kuak Y C. Narrow band excitation of a nonlinear oscillator[J]. Journal of Applied Mechanics, 1976,43(2): 340 - 344.
[7] Grigoriu M. Probabilistic analysis of response of Duffing oscillator to narrow band stationary Gaussian excitation[A]. In: E H Dowell Ed. Proceedings of First Pan-American Congress of Applied Mechanics [C]. Rio de Janeiro: Brazil, 1989.
[8] Davis H G, Liu Q. The response probability density function of a Duffing oscillator with random narrow band excitation[J]. Journal of Sound and Vibration, 1990,139(1): 1 - 8.
[9] Kapitaniak T. Stochastic response with bifurcations to non-linear Duffing's oscillator[J]. Journal of Sound and Vibration, 1985,102(3):440 - 441.
[10] Fang T, Dowell E H. Numerical simulations of jump phenomena in stable Duffing systems[J]. International Journal of Nonlinear Mechanics, 1987, 22(2):267 - 274.
[11] Zhu W Q, Lu M Q, Wu Q T. Stochastic jump and bifurcation of a Duffing oscillator under narrowband excitation[J]. Journal of Sound and Vibration, 1993,165(2):285 - 304.
[12] Wedig W V. Invariant measures and Lyapunov exponents for generalized parameter fluctuations[J]. Structural Safety, 1990,8(1): 13 - 25.
[13] Nayfeh A H. Introduction to Perturbation Techniques [M]. New York: Wiley, 1981.
[14] 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.
[15] 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.
[16] 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.
[17] ZHU Wei-qiu. Random Vibration[M]. Beijing:Science Press,1992. (in Chinese)

RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION

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