Nonstationary probability densities of system response of strongly nonlinear single-degree-of-freedom system subject to modulated white noise excitation 被引量：1

Nonstationary probability densities of system response of strongly nonlinear single-degree-of-freedom system subject to modulated white noise excitation

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摘要 The nonstationary probability densities of system response of a single-degree- of-freedom system with lightly nonlinear damping and strongly nonlinear stiffness subject to modulated white noise excitation are studied. Using the stochastic averaging method based on the generalized harmonic functions, the averaged Fokl^er-Planck-Kolmogorov equation governing the nonstationary probability density of the amplitude is derived. The solution of the equation is approximated by the series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. According to the Galerkin method, the time-dependent coefficients can be solved from a set of first-order linear differential equations. Then, the semi-analytical formulae of the nonstationary probability density of the amplitude response as well as the nonstationary probability density of the state response and the statistic moments of the amplitude response can be obtained. A van der Pol-Duffing oscillator subject to modulated white noise is given as an example to illustrate the proposed procedures. The effects of the system parameters, such as the linear damping coefficient and the nonlinear stiffness coefficient, on the system response are discussed. The nonstationary probability densities of system response of a single-degree- of-freedom system with lightly nonlinear damping and strongly nonlinear stiffness subject to modulated white noise excitation are studied. Using the stochastic averaging method based on the generalized harmonic functions, the averaged Fokl^er-Planck-Kolmogorov equation governing the nonstationary probability density of the amplitude is derived. The solution of the equation is approximated by the series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. According to the Galerkin method, the time-dependent coefficients can be solved from a set of first-order linear differential equations. Then, the semi-analytical formulae of the nonstationary probability density of the amplitude response as well as the nonstationary probability density of the state response and the statistic moments of the amplitude response can be obtained. A van der Pol-Duffing oscillator subject to modulated white noise is given as an example to illustrate the proposed procedures. The effects of the system parameters, such as the linear damping coefficient and the nonlinear stiffness coefficient, on the system response are discussed.

作者金肖玲黄志龙梁以德

机构地区 Department of Mechanics Zhejiang University Department of Electronic Engineering Department of Civil and Architectural Engineering City University of Hong Kong

出处《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第11期1389-1398,共10页 应用数学和力学（英文版）

基金 Project supported by the National Natural Science Foundation of China(No.11025211) the Zhejiang Provincial Natural Science Foundation of China(No.Z6090125) the Special Fund for National Excellent Ph.D.Dissertation and Research Grant Council of Hong Kong City(No.U115807)

关键词 nonstationary probability density modulated white noise stochastic averaging method Galerkin method nonstationary probability density, modulated white noise stochastic averaging method, Galerkin method

分类号 O327 [理学—一般力学与力学基础]

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