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Technical Brief

Stationary Solution of Duffing Oscillator Driven by Additive and Multiplicative Colored Noise Excitations

[+] Author and Article Information
Siu-Siu Guo

School of Civil Engineering,
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

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 139(2), 024502 (Feb 15, 2017) (4 pages) Paper No: VIB-16-1289; doi: 10.1115/1.4035308 History: Received June 09, 2016; Revised November 13, 2016

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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Figures

Grahic Jump Location
Fig. 1

PDF of displacement for Duffing system under OU processes with τ3 = τ4 = 0.5 and D3 = D4 = 1

Grahic Jump Location
Fig. 2

Log(PDF) of displacement for Duffing system under OU processes with τ3 = τ4 = 0.5 and D3 = D4 = 1

Grahic Jump Location
Fig. 3

PDF of displacement for Duffing system under OU processes with τ3 = τ4 = 0.5 and D3 = D4 = 2

Grahic Jump Location
Fig. 4

Log(PDF) of displacement for Duffing system under OU processes with τ3 = τ4 = 0.5 and D3 = D4 = 2

Grahic Jump Location
Fig. 5

PDF of displacement for Duffing system under OU processes with τ3 = τ4 = 1 and D3 = D4 = 2

Grahic Jump Location
Fig. 6

Log(PDF) of displacement for Duffing system under OU processes with τ3 = τ4 = 1 and D3 = D4 = 2

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