fGn激励下非线性系统近似方法适用性的解析分析  

Analytical analysis on the applicability of an approximate method to nonlinear systems driven by fGn

作　　者：邓茂林[1] 朱位秋[1] DENG Mao-lin;ZHU Wei-qiu(Institute of Applied Mechanics,School of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]浙江大学航空航天学院应用力学研究所,浙江杭州310027

出　　处：《振动工程学报》2022年第5期1076-1083,共8页Journal of Vibration Engineering

基　　金：国家重点研发计划资助项目(2018YFC0809400)。

摘　　要：由于受分数高斯噪声(fGn)激励的非线性系统响应不再具有马尔科夫性,基于扩散过程的理论方法不能直接用于研究此类问题。作为近似方法,宽带噪声激励的拟哈密顿系统随机平均法已经被用于解决此类问题。虽然,该理论方法在响应预测和可靠性分析方面取得了较好的效果,但是到目前为止还没有做过对近似方法的误差和适用性的解析分析。在本研究中,将近似方法用于分析fGn激励下的单自由度非线性系统,得到了系统响应的近似解析解,再结合已报道的精确解析解,用渐近分析的方法进行了误差分析,从而对近似方法的适用性进行了论证,为将来能够进一步扩展近似方法的应用提供了理论依据。Due to the non-Markov property of response of a nonlinear system driven by fractional Gaussian noise(fGn),the diffu‐sion process theory cannot be applied.As an approximate method,the stochastic averaging method for multi-DOF strongly nonlin‐ear systems driven by wideband noise has been applied to study nonlinear systems driven by fGn.The results show that the approxi‐mate method is very effective in the response prediction and the reliability analysis.However,so far there has been no analytical analysis on the error and applicability of the approximate method.In the present paper,the approximate method is applied to study a single-DOF nonlinear system driven by fGn and some analytical solutions are obtained.By comparing with reported exact analyti‐cal solutions,the error analysis is performed and the applicability of approximate method is determined.The conclusion of the pres‐ent paper can be the theoretical foundation for further application of the approximate method.

关 键 词：非线性系统 宽带噪声 分数高斯噪声 拟哈密顿系统随机平均法 

分 类 号：O324[理学—一般力学与力学基础]