轴向运动三阶剪切变形梁自由振动的DQM分析  

DQM Analysis of Free Vibration of Axially Moving Third-order Shear Deformable Beams

作　　者：随岁寒 刘晓丽[1] 孟华[1] SUI Suihan;LIU Xiaoli;MENG Hua(School of Mechanical Engineering,Shangqiu Institute of Technology,Shangqiu,China 476000;Wuxi Jinyuanqi Information Technology Co.,Ltd.,Wuxi,China 214000)

机构地区：[1]商丘工学院机械工程学院,河南商丘476000 [2]无锡金元启信息技术科技有限公司,江苏无锡214000

出　　处：《温州大学学报（自然科学版）》2022年第4期40-46,共7页Journal of Wenzhou University(Natural Science Edition)

基　　金：国家自然科学基金项目(11972240);河南省高等学校青年骨干教师培养计划项目(2019GGJS280)。

摘　　要：基于三阶剪切变形梁理论和虚功原理推导轴向运动梁自由振动的控制方程.利用微分求积法离散控制方程得到以位移为基本未知量的代数方程组,将其整理成矩阵形式,得到的质量矩阵、陀螺矩阵和刚度矩阵均非方阵,且行数大于列数.为将各矩阵转化为方阵,借鉴最小二乘法思想,基于质量矩阵转化得到系统广义特征方程,经与传统微分求积法和ANSYS软件所得结果对比,证明本文方法的正确性.The governing equations of free vibration of axially moving beams are derived based on the third-order shear deformable theory and virtual work principle. The algebraic equations with the displacement as the basic unknown quantity are obtained by discretization of the governing equation through differential quadrature method and are arranged into matrix form. The corresponding mass matrix, gyromatrix and stiffness matrix are not square matrix, that is, the number of rows is greater than the number of columns. In order to transform each matrix into a square matrix, the least square method is referenced to obtain the generalized characteristic equation of the system using the mass matrix. The correctness of the proposed method is proved by comparison with the results obtained by the conventional differential quadrature method and ANSYS software.

关 键 词：轴向运动梁 自由振动 三阶剪切变形梁理论 微分求积法 

分 类 号：O326[理学—一般力学与力学基础]