多跨连续梁自由振动的动态有限元分析.pdfVIP

振动与冲击

第43卷第15期JOURNALOFVIBRATIONANDSHOCKVol.43No.152024

多跨连续梁自由振动的动态有限元分析

夏桂云，刘明唻，温睿

（长沙理工大学土木工程学院，长沙410114）

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。

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

中图分类号：TB123文献标志码：AD0I:10.13465/j.cnki.jvs.2024.15.018

Dynamicfiniteelementanalysisforfreevibrationofmulti-spancontinuousbeams

XIAGuiyun,LIUMingjian,WENRui

(SchoolofCivilEngineering,ChangshaUniversityofScienceandTechnology,Changsha410114,China)

Abstract:UsinghomogeneoussolutionstothedifferentialmotionequationofTimoshenkobeams,deformationsand

internalforcesofarbitrarycross-sectionwereexpressedbythenodaldisplacements.Whentheinternalforcesonendpoints

wereevaluated,thedynamicfiniteelementwasformulated.Dynamicfiniteelementhascharacteristicsofnotrelyingon

meshdensityandbeingabletocorrectlycalculatearbitrary-ordernaturalfrequencyandmodeshape.Incorporatingthe

generalstiffnessmatrixdeterminantbeingzero,frequencyequationsofmulti-spancontinuousTimoshenkobeamwith

uniformcross-sectionandequalspanof1-4spanswerederived.Freevibrationsofmulti-spancontinuousTimoshenko

beamswereanalyzed,andtheresultsshowedthatthenaturalfrequenciesofthecorrespondingsimply-supported

Timoshenkobeamarenaturalfrequenciesofmulti-spancontinuousTimoshenkobeams,andtheformersvibrationmodes

areextendedtoformvibrationmodesofthelatter;multi-spancontinuousTimoshenkobeamsh