任意形状板考虑初始荷载效应的动力特性有限元分析

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1、万方数据振动与冲击第33卷第12期JOURNALOFVIBRATIONANDSHOCKV01．33No．122014任意形状板考虑初始荷载效应的动力特性有限元分析周世军，刘德贵(重庆大学土木工程学院，重庆400045)摘要：基于板考虑初始荷载效应的动力控制微分方程，运用等参变换方法，提出了任意形状板考虑初始荷载效应影响的动力有限元分析方法，编制了相应程序。同时，为验证提出的有限元方法的正确性，分别运用伽辽金法、瑞利法求解了几种典型板考虑初始荷载效应的基频近似解和简支正方形板考虑初始荷载效应的前三阶频率近似解。对比验证

2、说明了提出的基于等参变换的任意形状板考虑初始荷载效应的动力有限元分析方法和频率近似解正确、有效。并通过计算分析，讨论了初始荷载大小、板的厚度等因素对板自振频率的影响，结果表明：初始荷载的存在提高了板的自振频率，并主要与荷载大小，板的跨厚比和边界约束条件有关。计算分析中应重视初始荷载效应对板的结构行为产生的影响，以做到精确分析和合理结构设计。关键词：初始荷载效应；等参变换；有限元；板；动力特性中图分类号：TU313文献标志码iADOI：10．13465／j．cnki．jVS．2014．12．003Finiteeleme

3、ntanalysisfordynamiccharacteristicsofarbitraryshapeplates、订thinitialloadsZHOUShi-jun，LIUDe—gui(SchoolofCivilEngineering，ChongqingUniversity，Chongqing400045，China)Abstract：Basedondynamicgoverningdifferentialequationsconsideringeffectofinitialloadsofflplate，thedy

4、namicfiniteelementmethod(FEM)foranalyzingtheeffectofinitialloadsonarbitraryshapeplateswaspresentedusingtheisoparametriccoordinatetransformationmethod．Toverifythemethod，theapproximatesolutionstothefundamentalfrequencyconsideringeffectofinitialloadsforaclampedsqu

5、areplate，asimplysupposedequilateraltriangleplate，aclampedellipseplate，aclampedcircularplateandasimplysuppoaedcircularplatewerederivedbyusingGalerkinmethod．Theapproximatesolutionstothefirstthreemodelfrequenciesofasimplysupposedsquareplatewitheffectofinitialloads

6、weresolvedusingRayleighmethod．ThefrequenciesobtainedwiththeFEMagreedwellwiththoseapproximatesolutions，thecorrectnessandeffectivenessofthepresentedFEMandthoseapproximatesolutionswereverifiedeachother．Theeffectofinitialloadsondynamiccharacteristicsofarbitraryplat

7、eswasanalyzedwiththepresentedFEM，usefulconclusionswereobtained．Itwasshownthattheeffectofinitialloadsimprovesthebendingstiffnessofaplateandraisesthenaturalfrequenciesofaplate；thekeyphysicalfactorscontrollingtheeffectofinitialloadsonplatesareinitialload，ratioofsp

8、antothicknessandboundaryconditionsetcofaplate；thiseffectofinitialloadsisnotnegligible，especially，inthinnerplatesorplateswithsmallerstiffness，moreattentionsshouldbepaidtothee