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时间:2020-03-27
《任意直角梯形截面梁扭转刚度的无穷级数解法(英文).pdf》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、第25卷第5期传感技术学报V01.25No.52012年5月CHINESE.IOURNALOFSENSORSANDACTUAT0RSMav2012InfiniteSeriesSolutionsfortheTorsionalRigidityofaPrismwithRight-AngledTrapezoidCross—SectionsYANGGang,HAOYilong,HUQifang,GAOChengchen(1.NationalKeyLaboratoryofScienceandTechnologyonMicro/NanoFabricatio
2、n,InstituteofMicroelectronics,PekingUniversityBeijing100871,China;2.ShenzhenGraduateSchool,PekingUniversity,ShenzhenGuangdong518055,China)Abstract:Thetorsionrigidityofanelasticbeamwithright-angledtrapezoidcrosssectionsandbaseanglesrangingfrom10。to80。isstudiedanalyticallyand
3、examinedthroughFEM(FiniteElementeMethod)simulation.Tosolvethisspecialcaseofthefreetorsionproblemsofelasticprisms(theSaint—Venantproblems)theinfiniteseriesmethodbasedontheBoussinesq’shydromechanicalassumptionsisadoptedandfirstlyreposedinthiswork.BycomparisonwiththeFEMsimulat
4、ionresults.theanalyticalonesgiveaprecisepredictionwitherrorslessthan3%inthestudyrange.Forthetorsionrigidityoftrapezoidcross—sectionsbeamwith54.74。baseangle,theanalyticalresultsgiveaprecisepredictionwitherrorslessthan1.5%.Keywords:Saint—Venantproblem;right—angledtrapezoidCRO
5、SS—sectionsbeam;torsionalrigidity;hydr0mechanicalassumption;infiniteseriesmethodEEACC:2575;0260doi:10.3969/j.issn.1004—1699.2012.05.008任意直角梯形截面梁扭转刚度的无穷级数解法术杨纲,郝一龙,胡启方,高成臣(1.北京大学微电子学研究所,微米/纳米加t技术国家级重点实验室,北京100871;2.北京大学深圳研究生院.广东深圳518055)摘要:分析研究截面为底角10。~80。直角梯形的弹性梁扭转刚度的解法,并用有
6、限元模拟进行了检验。为解决这一弹性梁自由扭转问题(圣维南问题)的特殊情形,在本文中首次采用了基于布赛乃斯克流体力学假设的无穷级数解法。分析解法与软件模拟的结果对比显示,在所研究的范围内其误差精度不超过3%。对于底角为54.74。的特殊直角梯形截面梁,该解法的精度误差小于1.5%。关键词:圣维南问题;直角梯形截面梁;扭转刚度;流体力学假设;无穷级数法中图分类号:TN305文献标识码:A文章编号:1004—1699(2012)05—0594—05Thestudyofthetorsionalresonancemodeofmicro—sectiont
7、opologicaloftrapezoidshapeswith54.74。basecantileverbeamsisofgreatvaluetotheadvancedandangles.Formerresearehergivesanalyticalsolutionforwidely-usedMEMSdevicesl1].Tl1esiliconstructuresthetorsionrigidityofprismwithtrapezoidcrosssectionwithtrapezoidalcross—sectionsoccurfrequent
8、lyinbothwith45。baseangleusingapproximatesolution.MEMSsensorsandICdevicessuchasAFMc
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