摩擦自激振动系统的非线性动力学特征与分岔控制研究

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1、天津大学博士学位论文摩擦自激振动系统的非线性动力学特征与分岔控制研究姓名：黄毅申请学位级别：博士专业：机械制造及其自动化指导教师：王太勇20081201ABSTRACTSelf-excitedvibrationsinducedbyfrictionwidelyexistinfieldsofengineeringanddailylife．Usually,theunwantedself-excitedvibrationscauseanearlywearofthecontactingpansofmachines．Itseemsthatuptonownotallthepossiblenonlin

2、earphenomenahavebeenproperlyunderstood．Especiallysuchconditionsasparameterchangeandinternalresonancehaveseldombeenconsideredinamultiple-degree—of-freedomsystem．Andstudyonnonlinearactivecontrolstrategyisjuststarted．111eaimofthispaperistodeeplyinvestigatenonlinearcharacteristicsandbifurcationcontr

3、olofself-excitedvibration，whichresultsinthefollowingconclusions．Basedonextensivestudiesonvariousself-excitedsystemswithfriction，atypical“mass·on·moving—belt'’modelisderivedandestablishedfordescribingfriction—inducedvibration．Thedynamicalmodellaysthefoundmionfordeepstudiesonnonlinearcharacteristi

4、csandbifurcationcontroIofself-excitedvibration．ThenthestabilityoftheestablishedsystemisanalyzedanalyticallyusingLyapunovtheories．Aftercalculatingequilibriumpointsofthesystemandanalyzingthestabilityofthem，crucialvelocityatwhichthesystembecomesunstableisobtainedeventually．Andtheapproximateanalytic

5、alsolutionsofthesystemarederivedbymeansofKBMmethod．Byanalyzingrelationshipbetweenparametersandvibrationsofthesystem，itisfoundthatnormalpressureratioplaysanimportantroleinself-excitedvibration．Consideredimportanteffectofinternalresonance，nonlineardynamicalbehaviorsofthesystemundernon—internalreso

6、nance．1：2internalresonanceand1：3internalresonanceconditionsarenumericallyinvestigatedrespectively．Anexperimentalbenchfortestingfrictionalself-excitedvibrationsisdesignedandbuiltup．Analyticalandexperimentalresultsshowthatinternalresonanceconditionplaysanimportantroleinthefriction—inducedself-exci

7、tedvibration．．+TheWashoutfiltertechniqueisusedtocontrolself-excitedvibrationcausedbyfriction．nepointatwhichHopfbifurcationtobeintroducedisanalyzedanddetermined．ThenthelinearcontrolgainofWashoutfilercontrolleriscalculatedacco