基于一阶剪切板理论的FGM板刚柔耦合动力学建模与仿真  

DYNAMIC MODELING AND SIMULATION OF FUNCTIONALLY GRADED MATERIALS PLATES BASED ON FIRST ORDER SHEAR PLATE THEORY

作　　者：杨兴 刘仁伟 侯鹏 章定国[2] Yang Xing;Liu Renwei;Hou Peng;Zhang Dingguo(Shanghai Institute of Spacecraft Equipment,Shanghai 200240,China;School of Sciences,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]上海卫星装备研究所,上海200240 [2]南京理工大学理学院,南京210094

出　　处：《动力学与控制学报》2020年第4期33-43,共11页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11272155,11502113);中央高校基本科研业务费专项基金(30917011103)。

摘　　要：对作大范围运动功能梯度材料(functionally graded materials,FGM)厚板的刚柔耦合动力学问题进行了研究,基于一阶剪切变形理论,从连续介质理论出发,计及了变形位移场中的二次耦合变形量,利用Lagrange方法推导了FGM厚板的刚柔耦合动力学方程,该方程适用于普通均质板和FGM板的动力学分析.采用20自由度矩形单元对变形场进行离散,对不同转速下的悬臂板进行动力学仿真,比较了本文建立的基于一阶剪切理论的模型和基于经典薄板理论的模型,验证了本文模型的正确性以及经典薄板理论的一些不足.研究了不同功能梯度指数下,FGM厚板的横向变形、速度响应频率和固有频率.结果表明,随着转速增大,剪切项对结构动力学行为影响变大;考虑横向剪切项的情况下,计算结果更偏柔性.The rigid-flexible coupling dynamics of a rectangular functionally graded thick plate undergoing large overall motion was investigated.Based on the first order shear deformation theory,both the transverse shear deformation and the quadratic coupling deformation were taken into account.The rigid-flexible coupling dynamic equations of the functionally graded plate were deduced by Lagrange equations.The finite element method was used to discretize the deformation field with a rectangular element having 20 degrees of freedom based on the classical thin plate theory.The dynamic simu⁃lations of the cantilever plate with different rotating speeds were carried out.The influences of function gradient index on the transverse deformation,velocity response frequency and natural frequency of the functionally graded thick plate were also discussed.The results showed that the impact of the shear deformation on structural dynamics becomes notable with an increase in the rotating speed,and the structure is more flexible as the shear deformation is taken into account.

关 键 词：一阶剪切变形 功能梯度材料 有限元 动力刚化 

分 类 号：TB34[一般工业技术—材料科学与工程]