摘要
借助理论分析和数值仿真,研究了二维绝对节点坐标低阶梁单元和高阶梁单元模态参数。推导了考虑泊松效应的低阶和高阶梁单元1阶厚度固有频率解析解。基于广义特征方程获得了绝对节点坐标剪切梁单元的弯曲、轴向、剪切和厚度四种固有频率和固有振型。以简支梁结构为实例,分析了剪切梁单元多项式位移模式对弯曲、轴向、剪切和厚度四种固有频率和固有振型的作用规律。研究结果表明:绝对节点坐标剪切梁单元高阶多项式位移模式需要同时引入横向和纵向高阶项x2和y2,它们主要影响的是弯曲和轴向模态参数,对剪切和厚度模态参数影响较小,且低阶和高阶单元1阶厚度固有频率和它们的解析解均比较接近。
With the help of theoretical analysis and numerical simulation,the modal parameters of the two⁃dimensionally low⁃order beam elements and high⁃order beam elements based on the absolute nodal coordinate formulation were studied.The analytical solution of the first⁃order thickness natural frequency of low⁃order and high⁃order beam elements considering the Poisson effect was derived.Based on the generalized characteristic equation,four natural frequencies and natural modes of bending,axial,shear and thickness of the shear beam element based on the absolute nodal coordinate formulation were obtained.Taking a simply supported beam structure as an example,the effects of the polynomial displacement field of the shear beam element on the four natural frequencies and natural modes of bending,axial,shear and thickness were analyzed.The results show that the polynomial displacement field of the shear beam element needs to introduce both the horizontal and vertical high⁃order terms x2 and y2.They mainly affect the bending and axial modal parameters,but have little effect on the shear and thickness modal parameters,and first⁃order thickness natural frequencies of the lower⁃order and higher⁃order beam elements is relatively close to the derived analytical solutions of first⁃order thickness natural frequencies.
作者
周川
赵春花
独亚平
郭嘉辉
张立强
ZHOU Chuan;ZHAO ChunHua;DU YaPing;GUO JiaHui;ZHANG LiQiang(School of Mechanical and Automotive Engineering,Shanghai University of Engineering Science,Shanghai 201620,China)
出处
《机械强度》
CAS
CSCD
北大核心
2022年第6期1419-1425,共7页
Journal of Mechanical Strength
基金
国家自然科学基金项目(51775328)资助。
关键词
绝对节点坐标法
多项式位移模式
固有频率
固有振型
剪切梁单元
Absolute nodal coordinate formulation
Polynomial displacement field
Natural frequency
Natural mode
Shear deformable beam element
