基于绝对节点坐标法薄板结构振动特性分析  

Analysis of vibration characteristics of thin plate structures based on absolute nodal coordinate formulation

作　　者：赵鑫 伍松[1,2] 伍炜 曲汉龙 牛彩云[1] ZHAO Xin;WU Song;WU Wei;QU Hanlong;NIU Caiyun(School of Mechanical and Automotive Engineering,Guangxi University of Science and Technology,Liuzhou 545616,China;Guangxi Key Laboratory of Automobile Component and Vehicle Technology(Guangxi University of Science and Technology),Liuzhou 545616,China;Liuzhou Zhanhong Technology Co.,Ltd.,Liuzhou 545006,China)

机构地区：[1]广西科技大学机械与汽车工程学院,广西柳州545616 [2]广西汽车零部件与整车技术重点实验室(广西科技大学),广西柳州545616 [3]柳州市展虹科技有限公司,广西柳州545006

出　　处：《广西科技大学学报》2024年第4期25-34,共10页Journal of Guangxi University of Science and Technology

基　　金：国家自然科学基金项目(51665006);广西汽车零部件与整车技术重点实验室自主研究课题(2017GKLACVTZZ01)资助。

摘　　要：为研究柔性结构大变形问题,采用绝对节点坐标法(absolute nodal coordinate formulation,ANCF)对大变形柔性体结构进行建模。该方法由变形梯度和格林-拉格朗日应变来描述结构的运动以及变形,通过斜率矢量替代传统有限元法中的广义节点坐标,可直接用于解决结构中较复杂的大位移、大转动和大变形问题。根据绝对节点坐标法原理,研究薄板单元以及全参数板单元的振动特性,利用连续介质力学推导出单元的广义弹性力矩阵和切线刚度矩阵,由此建立板单元的动力学方程。利用MATLAB软件分别对薄板单元和全参数板单元进行自由模态分析,并将其仿真结果与ANSYS结果进行比较,同时通过牛顿迭代法验证2种板单元的收敛性。结果表明,消除厚度振荡影响的降阶薄板单元比全参数板单元有更好的精度和收敛特性,在针对模态分析的结构上,通过固有频率对比数据得出误差基本一致,从而单元的正确性得到验证,为后续研究和应用提供理论基础。To investigate large deformation problem in flexible structures,this paper adopts the absolute nodal coordinate formulation(ANCF)to model the large deformation of flexible bodies.This method describes the motion and deformation of structures using the deformation gradient and Green-Lagrange strain,replacing the generalized nodal coordinates in traditional finite element methods with the slope vector.It can be directly used to solve complex problems of large displacement,rotation,and deformation in structures.Based on the principles of the absolute nodal coordinate formulation,the vibrational characteristics of thin plate elements and fully parameterized plate elements are studied.The generalized elastic moment matrix and tangent stiffness matrix of the elements are derived using continuum mechanics,and the dynamic equations of the plate elements are established.Free modal analysis of thin plate elements and fully parameterized plate elements is conducted using MATLAB software,and the simulation results are compared with those from ANSYS.Additionally,the convergence of the two types of plate elements is verified using the Newton iteration method.The results show that the reduced-order thin plate elements which eliminate the effect of thickness oscillations exhibit better accuracy and convergence characteristics than the fully parameterized plate elements.In structural modal analysis,the error obtained by comparing natural frequencies is essentially consistent,validating the correctness of the elements and providing a theoretical basis for subsequent research and applications.

关 键 词：绝对节点坐标法(ANCF) 固有频率 模态分析 

分 类 号：TB123[理学—工程力学]