轴向运动复合材料圆柱壳的非线性振动研究  

STUDY ON THE NONLINEAR VIBRATION OF AXIALLY MOVING CYLINDRICAL SHELLS MADE FROM COMPOSITES

作　　者：李健[1,2] 郭星辉[2] 杨坤[2] 颜云辉[1] 

机构地区：[1]东北大学机械工程与自动化学院,沈阳110004 [2]东北大学理学院,沈阳110004

出　　处：《固体力学学报》2011年第2期176-185,共10页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金和上海宝钢集团公司联合资助(50574019);国家"863"计划项目(2008AA04Z135);国家科技部重大基础研究前期研究专项(2003CCA03900)资助

摘　　要：采用Runge-Kutta法和多尺度法对轴向运动分层复合材料薄壁圆柱壳的非线性振动特性进行了研究.首先根据层合壳理论建立轴向运动分层复合材料薄壁圆柱壳的波动方程,利用Galerkin法对方程进行离散,得到相互耦合模态方程组.然后应用Runge-Kutta法分析了不同参数条件下的幅频特性曲线,得到了系统由于固有频率接近所导致的内共振现象,以及系统呈现软特性等非线性特性.最后采用多尺度法进行了系统1:1内共振时的近似解析分析,对系统在不同参数下的振动研究表明,激振力幅值、阻尼、速度等参数对位移响应幅值、共振区间、模态间的耦合度及系统软特性程度均有影响,其结论与数值计算结果一致,并同时对解的稳定性进行了研究.Runge-Kutta and multiscale methods are used to study nonlinear vibration characteristics of axially moving,multi-layered cylindrical shells made from composites.A nonlinear wave vibration equation of the thin cylindrical shell made from composites is established firstly,taking multilayer and axially movement into account,based on layered shell theory.The equation is discretized by Galerkin＇s method and then interconnected modal equations are obtained.Runge-Kutta method is applied to analyze curves of amplitude-frequency characteristic with different parameters.The results show some nonlinear properties of the system such as the phenomenon of internal resonance due to two closed natural frequencies and soft feature.Finally,multiscale method is introduced to investigate approximate analytical solutions of the system with 1：1 internal resonance.The results indicate that excitation amplitude,damping and speed can affect response amplitude,range of interval resonance,coupling between two modes and soft feature of the system.Conclusions with different methods coincide and stability of the system is further discussed.

关 键 词：RUNGE-KUTTA法 多尺度法 分层 1:1内共振 稳定性 

分 类 号：O322[理学—一般力学与力学基础]