作定轴转动悬臂板的动力学建模及其动态特性分析  

Dynamic Modeling and Modal Analysis of a Cantilever Plate Rotating Around a Rigid Hub

作　　者：刘利军[1,2] 张志谊[1] 杜冬[1] 华宏星[1] 

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]沪东重机有限公司技术中心,上海200129

出　　处：《机械科学与技术》2009年第9期1153-1156,共4页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目(10672099)资助

摘　　要：总结了作旋转运动的梁/板悬臂结构的动力学建模及发展过程。针对绕定轴转动的板类悬臂结构,用伸长变量和笛卡儿变量等混合变形变量表示其位移场,经过有限元离散,由第二类La-grange方程导出转动悬臂板的运动微分方程。对绕定轴转动的刚-柔耦合悬臂板结构的动态特性及振动控制进行了数值仿真计算,根据所得结果,讨论了长宽比、转速对转动悬臂板模态特性的影响,揭示了板的固有频率特征值"轨迹转向"和"交叉"现象;利用压电材料作为作动元件,实现了对转动悬臂板的振动主动控制,并给出了脉冲激励作用下控制前后的时间-位移幅值曲线。Dynamic modeling of a cantilever beam and plate around a rigid hub is presented. According to platelike structures rotating around a rigid hub, stretch variables and Cartesian variables are combined into hybrid deformation variables to express structural displacements. Through finite element discretization, partial motion equations of a rotating cantilever plate are derived by the second kind of Lagrange equations. Consequently, numerical simulation is carried out to calculate the dynamics characteristics and vibration suppression of rigid-flexible coupling cantilever plate rotating about its normal. According to the simulation results, the effect of aspect ratios and rotating speeds on the modal characteristic of the rotating cantilever plate are discussed. Frequencies loci veering and crossing phenomena are exhibited and discussed in detail. Finally, piezoelectric materials acting as actuators are used to attenuate the vibration of the rotating cantilever plate. Uncontrolled and controlled time-displacement curves of the rotating cantilever plate under impulse power are given.

关 键 词：转动悬臂板 动力刚化效应 频率特征值轨迹转向及交叉 振动控制 

分 类 号：TH113[机械工程—机械设计及理论] V214.3[航空宇航科学与技术—航空宇航推进理论与工程]