静电梳状硅微单侧直脚谐振器的力学性能

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1、第45卷第5期机械工程学报Vo1．45NO．52009年5月JOURNALOFMECHANICALENGINEERINGMay2009DoI：10．3901／JME．2009．O5．049静电梳状硅微单侧直脚谐振器的力学性能冰沈雪瑾(上海大学机电工程与自动化学院上海200072)摘要：建立单侧支撑直脚型静电梳状硅微谐振器的三次超静定简化力学模型，给出该模型中谐振频率、弹性系数和横向最大位移的计算公式。与五次超静定系统的双侧支撑直脚型静电梳状硅微谐振器的各力学性能参数的计算公式对比发现它们有显著差别。分析表

2、明，与双侧支撑直脚型静电梳状硅微谐振器显著不同，单侧支撑直脚型静电梳状硅微谐振器的谐振频率、弹性系数、横向最大位移会随两根支撑梁的间距变化而改变，并当此间距超过某一值后，上述三变量的变化均很小且趋向于一定值。同样，后者的谐振频率会随支撑梁厚度的变化而单调改变，这也是前者所没有的现象。为此从两者因为超静定次数不同而约束冗余度不同的角度，对此现象进行了物理意义上的解释。经与试验结果对比，单侧支撑直脚型静电梳状硅微谐振器横向谐振频率的理论值与实测值吻合较好，最大误差为12．07％。关键词：微型机电系统静电硅微谐

3、振器单侧支撑性能分析中图分类号：TH112TN305MechanicalPerformanceofMicroOne--sidedStraight·-legBeamResonatorSHENXuejin(SchoolofMechatronicsEngineeringandAutomation，ShanghaiUniversity,Shanghai200072)Abstract：ThelateralVibrationofmicroresonatorsuspendedwithone·-sidestraight—

4、-legbeamsissimplemodeledinasuperfluoussystemwiththreeunknownvariables．Methodsaregiventocalculatetheresonantfrequency,elasticcoeficientandlateraldisplacement．Comparingwiththemicroresonatorsuspendedwithdouble-sidestraight—legbeamsthatisasuperfluoussystemwit

5、hfiveunknownvariables，itisfoundthatthemechanicalpropertiesoftheformerarequitediferentwiththatoflater．Itisclearlydiferentfromthemicroresonatorsuspendedwithdouble-·sidestraight—·legbeamsfromtheanalysisresultsthattheresonantfrequency,elasticcoeficientandlate

6、raldisplacementwillchangewiththevariationofdistancebetweenthetwostraight—legbeamsinmicroresonatorsuspendedwithone—sidestraight—legbeams．Afterthedistanceexceedsacertainvalue．thechangeofalltheabovethreevariablesisverysmallandtendstoafixednumber．Similarly,th

7、eresonantfrequencyalsowillchangewiththevariationofbeamthicknessinlater，butthereisnosuchphenomenonintheformer．Soanexplanationisgivenaccordingtothediferentredundanceforthetwodiferentsuperfluoussystems．Thetheoreticalresonantfrequenciesofmicroresonatorssuspen

8、dedwithone—sidestraight-legbeamsarecoincidentwiththemeasuredvalues．Thebiggesterrorbetweenthemis12．07％．Theaboveresultsprovidereferenceforthestructuredesignofmicroresonator．Keywords：Microelectromechanicalsystems(MEMS)