Analytical studies of nonlinear systems driven by colored noise are quite involved. If the inertia of the system is included in analysis, the results are physically realistic although the problem becomes more complex. Research along this line is in progress and this paper is an effort to study a nonlinear oscillator excited by correlated noise. The work delves on the Duffing oscillator driven by exponentially correlated noise. The colored Fokker-Planck equation is derived and the method of systematic adiabatic expansion is used to obtain the reduced probability density function from which the second-order moments are evaluated for different values of system parameters. Numerical simulation is carried out by generating colored noise using the spectral method. In the region where perturbation is valid, the results of adiabatic expansion agree very well with that of Monte Carlo simulation.
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December 1996
Technical Papers
Analytical Study of the Duffing Oscillator Excited by Colored Noise Using a Systematic Adiabatic Expansion
M. M. Wu,
M. M. Wu
Program in Mechanics, Materials and Structures, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544
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K. Y. R. Billah,
K. Y. R. Billah
Program in Mechanics, Materials and Structures, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544
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M. Shinozuka
M. Shinozuka
Program in Mechanics, Materials and Structures, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544
Search for other works by this author on:
M. M. Wu
Program in Mechanics, Materials and Structures, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544
K. Y. R. Billah
Program in Mechanics, Materials and Structures, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544
M. Shinozuka
Program in Mechanics, Materials and Structures, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544
J. Appl. Mech. Dec 1996, 63(4): 1027-1032 (6 pages)
Published Online: December 1, 1996
Article history
Received:
June 8, 1995
Revised:
May 15, 1996
Online:
October 26, 2007
Citation
Wu, M. M., Billah, K. Y. R., and Shinozuka, M. (December 1, 1996). "Analytical Study of the Duffing Oscillator Excited by Colored Noise Using a Systematic Adiabatic Expansion." ASME. J. Appl. Mech. December 1996; 63(4): 1027–1032. https://doi.org/10.1115/1.2787224
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