一类非线性磁流变系统的混沌动力学特征  

CHAOTIC CHARACTERS OF NONLINEAR SYSTEM BASED ON MAGNETORHEOLOGICAL DAMPER

作　　者：杨新伟[1] 田瑞兰[2] 满洪高[1] 

机构地区：[1]石家庄铁路职业技术学院交通系,石家庄050041 [2]石家庄铁道学院非线性动力学研究中心,石家庄050043

出　　处：《机械强度》2010年第4期546-549,共4页Journal of Mechanical Strength

基　　金：国家自然科学基金(10672116);河北省教育厅基金(2009470;2009478)资助项目~~

摘　　要：基于Silnikov定理,讨论一类基于磁流变阻尼器非线性系统的混沌特性。借助卡尔达诺公式和微分方程组级数解,分别讨论该系统的特征值问题和同宿轨道的存在性,进而比较严密地证明该系统Silnikov型Smale混沌的存在性,并给出发生Silnikov型Smale混沌所需条件。利用数值模拟得到该类磁流变阻尼器非线性系统的相轨迹图、Lyaponov指数谱和Lyaponov维数,进一步验证该非线性系统存在奇怪吸引子。Based on the Silnikov criterion, the chaotic characteristics of a nonlinear magneto-rheological damper were studied. Using Cardano formula and series solution of differential equation, the eigenvalue problem and examined the existence of homoclinie orbit first were solved. Then, the existence of Silnikov-type chaos and derived the conditions for onset of chaos were examined. Through numerical simulations, the Silnikov-type homoelinic orbit, together with the Lyapunov expenent spectrum and the Lyapunov dimensions for chaos were obtained in the nonlinear system, which further ascertaining the foregoing qualitative analysis.

关 键 词：磁流变阻尼器 混沌系统 LYAPUNOV指数 Silnikov定理 非线性 

分 类 号：O322[理学—一般力学与力学基础] O193[理学—力学]