壳板凸肩叶片的分岔特性研究  

A study on the bifurcation characteristics for shrouded blade of cylindrical panel

作　　者：李红影[1,2] 谢里阳[1] 郭星辉[2] 

机构地区：[1]东北大学机械工程与自动化学院,辽宁沈阳110004 [2]东北大学应用力学研究所,辽宁沈阳110004

出　　处：《振动工程学报》2012年第3期260-267,共8页Journal of Vibration Engineering

基　　金：创新团队发展计划(IRT0816)

摘　　要：研究壳板凸肩叶片的静态和全局动态分岔。应用Donnell’s简化壳理论建立了壳板凸肩叶片的非线性振动微分方程,并考虑了几何非线性、阻尼、凸肩接触面正压力、摩擦力等因素。运用伽辽金方法对非线性振动微分方程离散化,应用平均法对离散后模态方程组进行解析分析,获得系统主共振情况下的平均方程和分岔方程。利用奇异性理论,得到了系统的转迁集和分岔图。通过研究平均方程的全局行为,得到了壳板凸肩叶片系统参数在各区域变化时系统周期解的变化过程及其具有的非线性动力学特性。研究壳板凸肩叶片的分岔特性可以为壳板凸肩叶片系统的动力学优化设计以及稳定性控制提供理论依据。The static and global dynamic bifurcations for shrouded blade of cylindrical panel are studied in the paper.Using Donnell’s nonlinear shallow-shell theory,the non-linear differential equation of vibration is obtained and is discretized by Galerkin method,in which frictions between shrouds,damping,normal pressures on contact surface and geometric nonlinearity are taken into account.The averaging method is applied to analytically study the system,and averaged equation and bifurcation one are obtained in the case of primary resonance.Using singularity theory the transition sets and bifurcation diagrams are presented.By studying global behaviors of averaged equation,the changing process of the periodic solutions for averaged system and its nonlinear dynamic characteristics are obtained,while the systematic parameters of shrouded blade of cylindrical panel change in different sections.The study on the bifurcation characteristics for shrouded blade of cylindrical panel can therefore provide a theoretical basis for optimal dynamic design and stability control of blades.

关 键 词：壳板凸肩叶片 非线性 摩擦 平均法 分岔 

分 类 号：O322[理学—一般力学与力学基础]