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Research Papers

Probabilistic Solutions of Stochastic Oscillators Excited by Correlated External and Parametric White Noises

[+] Author and Article Information
Siu-Siu Guo

International Center for Applied Mechanics,
State Key Laboratory for Strength
and Vibration of Mechanical Structure,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: siusiuguo@mail.xjtu.edu.cn

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 29, 2013; final manuscript received January 12, 2014; published online February 21, 2014. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 136(3), 031003 (Feb 21, 2014) (7 pages) Paper No: VIB-13-1384; doi: 10.1115/1.4026594 History: Received October 29, 2013; Revised January 12, 2014; Accepted January 13, 2014

The stationary probability density function (PDF) solution of random oscillators with correlated additive and multiplicative Gaussian excitations is investigated in this paper. The correlation between additive and multiplicative Gaussian excitations is taken into account. As a result, the generalized Fokker-Planck-Kolmogorov (FPK) equation is expressed with the independent part and the correlated part, which can be solved by the exponential-polynomial closure (EPC) method. The linear and nonlinear oscillators under correlated additive and multiplicative Gaussian white noise excitations are investigated. Two cases of different correlated additive and multiplicative excitations are considered. Compared with the results in the case of independent external and parametric excitations, unsymmetrical PDFs and nonzero means of system responses can be obtained.

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Figures

Grahic Jump Location
Fig. 1

Logarithm of PDFs of the oscillator responses in example 1

Grahic Jump Location
Fig. 2

Logarithm of PDF of the oscillator responses with different correlations of white noise in example 1. ( − · −) EPC (n = 6) approximation, (−) numerical simulation.

Grahic Jump Location
Fig. 3

Logarithm of PDF of displacement with varied correlated coefficients in example 1

Grahic Jump Location
Fig. 4

Logarithm of PDFs of the oscillator responses in example 2

Grahic Jump Location
Fig. 5

Logarithm of PDFs of the oscillator responses with different correlations of white noises in example 2. (− · −) EPC (n = 6) approximation, (−) numerical simulation.

Grahic Jump Location
Fig. 6

Logarithm of PDF of displacement with varied correlated coefficients in example 2

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