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.
Probabilistic Solutions of Stochastic Oscillators Excited by Correlated External and Parametric White Noises
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.
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Guo, S. (February 21, 2014). "Probabilistic Solutions of Stochastic Oscillators Excited by Correlated External and Parametric White Noises." ASME. J. Vib. Acoust. June 2014; 136(3): 031003. https://doi.org/10.1115/1.4026594
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