Physical and engineering systems are often subjected to combined harmonic and random excitations. The random excitation is often modeled as Gaussian white noise for mathematical tractability. However, in practice, the random excitation is nonwhite. This paper investigates the stationary response probability density of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. By using generalized harmonic functions, a new stochastic averaging procedure for estimating stationary response probability density of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations is developed. The damping can be linear and (or) nonlinear and the excitations can be external and (or) parametric. After stochastic averaging, the system state is represented by two-dimensional time-homogeneous diffusive Markov processes. The method of reduced Fokker–Planck–Kolmogorov equation is used to investigate the stationary response of the vibration system. A nonlinearly damped Duffing oscillator is taken as an example to show the application and validity of the method. In the case of primary external resonance, based on the stationary joint probability density of amplitude and phase difference, the stochastic jump of the Duffing oscillator and P-bifurcation as the system parameters change are examined for the first time. The agreement between the analytical results and those from Monte Carlo simulation of original system shows that the proposed procedure works quite well.
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October 2008
Research Papers
Stochastic Averaging of Strongly Nonlinear Oscillators Under Combined Harmonic and Wide-Band Noise Excitations
Y. J. Wu,
Y. J. Wu
School of Information Science and Engineering,
e-mail: yongjunwu@ecust.edu.cn
East China University of Science and Technology
, Shanghai 200237, P.R.C.
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W. Q. Zhu
W. Q. Zhu
Search for other works by this author on:
Y. J. Wu
School of Information Science and Engineering,
East China University of Science and Technology
, Shanghai 200237, P.R.C.e-mail: yongjunwu@ecust.edu.cn
W. Q. Zhu
J. Vib. Acoust. Oct 2008, 130(5): 051004 (9 pages)
Published Online: August 12, 2008
Article history
Received:
January 11, 2007
Revised:
January 8, 2008
Published:
August 12, 2008
Citation
Wu, Y. J., and Zhu, W. Q. (August 12, 2008). "Stochastic Averaging of Strongly Nonlinear Oscillators Under Combined Harmonic and Wide-Band Noise Excitations." ASME. J. Vib. Acoust. October 2008; 130(5): 051004. https://doi.org/10.1115/1.2948382
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