多跨连续梁自由振动的动态有限元分析  

Dynamic finite element analysis for free vibration of multi-span continuous beams

作　　者：夏桂云[1] 刘明暕 温睿 XIA Guiyun;LIU Mingjian;WEN Rui(School of Civil Engineering,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学土木工程学院,长沙410114

出　　处：《振动与冲击》2024年第15期150-159,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(51278072);湖南省教育厅重点项目(22A0223)。

摘　　要：利用Timoshenko梁振动微分方程的奇次解,建立了单元任意截面的变形、内力与节点位移的关系,取端点截面的内力得到动态有限元列式。动态有限元具有不依赖网格密度、可准确计算任意阶次的振动频率和振型等特点。利用动态有限元刚度矩阵行列式为0条件,推导出1~4跨等截面等跨径的多跨连续梁频率方程。分析了多跨连续梁的自由振动,结果表明:相应简支梁的频率为多跨连续梁的固有频率、振型经扩展后为多跨连续梁的振型;多跨连续梁的振动有第二频谱现象和梁高振动特征。Using homogeneous solutions to the differential motion equation of Timoshenko beams,deformations and internal forces of arbitrary cross-section were expressed by the nodal displacements.When the internal forces on endpoints were evaluated,the dynamic finite element was formulated.Dynamic finite element has characteristics of not relying on mesh density and being able to correctly calculate arbitrary-order natural frequency and mode shape.Incorporating the general stiffness matrix determinant being zero,frequency equations of multi-span continuous Timoshenko beam with uniform cross-section and equal span of 1-4 spans were derived.Free vibrations of multi-span continuous Timoshenko beams were analyzed,and the results showed that the natural frequencies of the corresponding simply-supported Timoshenko beam are natural frequencies of multi-span continuous Timoshenko beams,and the former’s vibration modes are extended to form vibration modes of the latter;multi-span continuous Timoshenko beams has the second frequency spectrum phenomenon and the beam height vibration feature.

关 键 词：动态有限元 多跨连续梁 频率方程 模态 第二频谱 梁高振动 

分 类 号：TB123[理学—工程力学]