基于绝对节点坐标法变截面柔性梁运动稳定性研究  

Study on Motion Stability of Variable Cross-Section Flexible Beams Based on the Absolute Nodal Coordinate Formulation

作　　者：罗晶晶 余海东[1] 赵春璋[1,2] 王皓[1,2] LUO Jingjing YU Haidong ZHAO Chunzhang WANG Hao(State Key Laboratory of Mechanical System and Manufacture for Thin-walled Structures, Shanghai Vibration Shanghai Key Laboratory of Digital Jiao Tong University, Shanghai 200240, China)

机构地区：[1]上海交通大学机械系统与振动国家重点实验室,上海200240 [2]上海交通大学上海市复杂薄板结构数字化制造重点实验室,上海200240

出　　处：《上海交通大学学报》2017年第10期1174-1180,共7页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金项目(51275292);国家重点基础研究发展基金项目(2014CB046600)资助

摘　　要：基于绝对节点坐标法,考虑变截面梁单元的几何边界特征,利用非线性介质力学方法推导其刚度矩阵,进而建立柔性梁结构动力学方程.基于梁结构运动过程中状态空间方程和Lyapunov理论,提出变截面柔性梁结构运动及稳定性判定方法,研究了材料属性与变截面对梁结构空间运动过程中稳定性的影响.结果表明:当材料弹性模量较小时,变截面梁的稳定性略优于等截面梁;当材料的弹性模量增大,等截面梁单元稳定性大大增加,而变截面梁单元所受影响甚微;当弹性模量的增加达到一定值后,等截面梁的运动也趋于稳定.The boundary features of the variable cross-section beams are taken into consideration and the stiffness matrix is derived based on the nonlinear continuum mechanics. A dynamic model of the beam is established by using the absolute nodal coordinate formulation. The state-space equation of the beam during motion is developed. Based on the Lyapunov theory a criterion of the motion stability of the flexible beams is proposed, and the effects of material properties and variable cross-sections are investigated. The results indicate that with a small elastic modulus, the variable cross-section beam shows a better stability than the constant cross-section beam. As the elastic modulus increases, the stability of the constant cross- section becomes better than that of the variable cross-section beam. When the elastic modulus reaches a certain value, the motion of constant cross-section beam becomes stable.

关 键 词：变截面柔性梁 大变形 稳定性 LYAPUNOV理论 

分 类 号：TH113.2[机械工程—机械设计及理论]