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1、第25卷第5期傳感技術(shù)學報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轉(zhuǎn)剛度的無窮級數(shù)解法術(shù)楊綱，郝一龍，胡啟方，高成臣(1．北京大學微電子學研究所，微米／納米加t技術(shù)國家級重點實驗室，北京100871；2．北京大學深圳研究生院．廣東深圳518055)摘要：分析研究截面為底角10?！?0。直角梯形的彈性梁扭轉(zhuǎn)剛度的解法，并用有
6、限元模擬進行了檢驗。為解決這一彈性梁自由扭轉(zhuǎn)問題(圣維南問題)的特殊情形，在本文中首次采用了基于布賽乃斯克流體力學假設(shè)的無窮級數(shù)解法。分析解法與軟件模擬的結(jié)果對比顯示，在所研究的范圍內(nèi)其誤差精度不超過3％。對于底角為54．74。的特殊直角梯形截面梁，該解法的精度誤差小于1．5％。關(guān)鍵詞：圣維南問題；直角梯形截面梁；扭轉(zhuǎn)剛度；流體力學假設(shè)；無窮級數(shù)法中圖分類號：TN305文獻標識碼：A文章編號：1004—1699(2012)05—0594—05Thestudyofthetorsionalresonancemodeofmicro—sectiont
7、opologicaloftrapezoidshapeswith54．74。basecantileverbeamsisofgreatvaluetotheadvancedandangles．Formerresearehergivesanalyticalsolutionforwidely-usedMEMSdevicesl1]．Tl1esiliconstructuresthetorsionrigidityofprismwithtrapezoidcrosssectionwithtrapezoidalcross—sectionsoccurfrequent
8、lyinbothwith45。baseangleusingapproximatesolution．MEMSsensorsandICdevicessuchasAFMc
