轴向移动悬臂梁高效动力学建模及频率响应分析  

AN EFFICIENT DYNAMIC MODELING METHOD OF AN AXIALLY MOVING CANTILEVER BEAM AND FREQUENCY RESPONSE ANALYSIS

作　　者：华洪良[1] 廖振强[1] 张相炎[1] Hua Hongliang;Liao Zhenqiang;Zhang Xiangyan(School of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学机械工程学院,南京210094

出　　处：《力学学报》2017年第6期1390-1398,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(51375241)

摘　　要：轴向移动梁动力学问题具有广泛的工程应用背景,如:机械手、机床主轴、武器身管等.计算轴向移动梁动力学响应是评估结构动力学性能以及最终指导结构设计的一个重要手段.采用Rayleigh-Ritz法、拉格朗日方程推导了轴向移动悬臂梁时变动力学方程.选取幂级数函数构造试函数对轴向移动系统动力问题进行求解.幂级数函数良好的积分与微分性能,使得推导容易以矩阵的形式快速进行,便于符号运算软件直接生成MATLAB程序.由于MATLAB基本数据单位为矩阵,符号软件生成的程序只需经过简单修改便可进行动力学计算.大大缩短了轴向移动梁从建模到动力学分析的时间,过程十分高效.通过四组算例,将本文方法计算得到的动力学响应与文献数据进行对比,对该方法准确性进行了验证,并给出了幂级数函数拟合阶数的选取原则.以此为基础,研究了轴向移动梁的频率响应特性.分为考虑重力与忽略重力两种情况,讨论了轴向振动幅度对其频率响应特性的影响.The dynamics of the axially moving beam has wide application in engineering,such as robot manipulators,machine tools and gun barrel,et al.Computing the dynamic response of axially moving beam is an important method to evaluate the dynamic performance and finally the structure design.The time-varying motion equations of the axially moving cantilever beam are derived using the Rayleigh-Ritz method and Lagrange's equation.The power series function is used to construct the trial function to solve the dynamic problem.Due to the good integral and differential performance of power series function,the derivation is easy to be carried out in the form of matrix.In this way,the symbolic computation software can generate the MATLAB program directly.And the generated MATLAB program can be used to conduct the dynamic computation with few modifications,because the basic data unit of MATLAB is matrix.The overall process is effciency and the time from dynamic modeling to computation is greatly reduced.Through four sets of numerical examples,the computational accuracy of the presented method is validated by comparing the dynamic responses with those from previous literatures.Then,the effects of fitting order of the power series function on computational accuracy are discussed.And the principle to select the fitting order of the power series function to achieve good convergence and computational accuracy is given.Based on the dynamic model,the effects of axial motion frequency on transverse vibration are studied.The effects of axial vibration amplitude on the frequency response characteristic are explored.And the difference between considering gravity and neglecting gravity effect are compared.

关 键 词：计算动力学 幂级数基函数 频响分析 轴向移动梁 

分 类 号：O313[理学—一般力学与力学基础]