A bistable Duffing oscillator subjected to additive and multiplicative Ornstein–Uhlenbeck (OU) colored excitations is examined. It is modeled through a set of four first-order stochastic differential equations by representing the OU excitations as filtered Gaussian white noise excitations. Enlargement in the state-space vector leads to four-dimensional (4D) Fokker–Planck–Kolmogorov (FPK) equation. The exponential-polynomial closure (EPC) method, proposed previously for the case of white noise excitations, is further improved and developed to solve colored noise case, resulting in much more polynomial terms included in the approximate solution. Numerical results show that approximate solutions from the EPC method compare well with the predictions obtained via Monte Carlo simulation (MCS) method. Investigation is also carried out to examine the influence of intensity level on the probability distribution solutions of system responses.
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April 2017
Technical Briefs
Stationary Solution of Duffing Oscillator Driven by Additive and Multiplicative Colored Noise Excitations
Siu-Siu Guo,
Siu-Siu Guo
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: siusiuguo@hotmail.com
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: siusiuguo@hotmail.com
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Qingxuan Shi
Qingxuan Shi
Professor
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: shiqx@xauat.edu.cn
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: shiqx@xauat.edu.cn
Search for other works by this author on:
Siu-Siu Guo
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: siusiuguo@hotmail.com
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: siusiuguo@hotmail.com
Qingxuan Shi
Professor
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: shiqx@xauat.edu.cn
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: shiqx@xauat.edu.cn
1Corresponding author.
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 9, 2016; final manuscript received November 13, 2016; published online February 15, 2017. Assoc. Editor: Mohammed Daqaq.
J. Vib. Acoust. Apr 2017, 139(2): 024502 (4 pages)
Published Online: February 15, 2017
Article history
Received:
June 9, 2016
Revised:
November 13, 2016
Citation
Guo, S., and Shi, Q. (February 15, 2017). "Stationary Solution of Duffing Oscillator Driven by Additive and Multiplicative Colored Noise Excitations." ASME. J. Vib. Acoust. April 2017; 139(2): 024502. https://doi.org/10.1115/1.4035308
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