Probability density function for stochastic response of non-linear oscillation system under random excitation |
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Authors: | Xufang Zhang Yimin Zhang Yuee Zhao |
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Institution: | a Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Canada N2l 3G1 b School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, PR China c Xinmin Normal College, Shenyang University, Shenyang 110300, PR China |
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Abstract: | Probability density function (PDF) of stochastic responses is a critical topic in uncertainty analysis. In this paper, orthogonal decomposition technique was extended to discuss non-stationary response of non-linear oscillator under random excitation. The PDF of stochastic reponses is represented by a set of standardized multivariable orthogonal polynomials. According to the Galerkin scheme, the original problem, which has to solve the Fokker-Planck-Kolmogorov (FPK) equation, was converted to a first-order linear ordinary differential equation, in terms of unknown time-dependent coefficients. Then, stationary and non-stationary PDFs of uncertainty responses were obtained. In numerical examples, first-order and second-order non-linear systems exposed to the Gaussian white noise were considered. Finally, the accuracy of the proposed method was demonstrated through appropriate comparisons to Monte-Carlo simulation and analytical results. |
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Keywords: | Probability density function Non-stationary response Non-linear stochastic vibration Multivariable orthogonal polynomial |
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