用复规范形法研究窄带随机动力系统  

Investigation of Narrow-Band Random Dynamic Systems by Complex Normal Form Method

作　　者：赵德敏[1] 张琪昌[1] 何学军[1] 

机构地区：[1]天津大学机械工程学院,天津300072

出　　处：《天津大学学报》2008年第3期267-270,共4页Journal of Tianjin University(Science and Technology)

基　　金：国家自然科学基金资助项目(10372068);教育部博士点基金资助项目(20060056005)

摘　　要：为了深入研究窄带噪声作用下随机动力系统的特性,将复规范形法用于窄带随机动力系统.研究了Duffing、Rayleigh和Van der pol方程在谐和与窄带随机参数激励联合作用下的主共振响应和稳定性.由复规范形法得到了此系统响应振幅和相位所满足的方程,再由摄动法分析了系统的主共振响应和稳定性,并用随机增维精细积分法验证了方程理论分析结果的正确性,用数值法计算了平凡解的Lyapunov指数曲面.结果表明,随着窄带随机扰动强度的增加,系统稳态解的相图从极限环变为扩散的极限环.研究证实了复规范形法用于窄带随机动力系统是有效的.In order to study the property of random dynamic systems excited by narrow-band noise, the complex normal form method was applied to narrow-band random dynamic systems. The principal resonance and stability of Duffing, Rayleigh and Van der pol oscillator under combined harmonic and narrow-band random parametric excitation were investigated. Equations of the amplitude and phase were obtained by using the complex normal form method. Then the perturbation method was used to analyze principal resonance and stability. The theoretical results were verified by stochastic precise integration method. The Lyapunov exponent three-dimensional surface was also obtained by numerical method. Theoretical analyses and numerical simulation showed that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. The results proved the applicability of the complex normal form method for narrow-band random dynamics systems.

关 键 词：窄带随机系统 复规范形法 参数主共振 最大LYAPUNOV指数 

分 类 号：O322[理学—一般力学与力学基础]