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1、2InternationalJournalofCOMADEM,10(3)July2007,PP.2-10RotorDynamicswithoutEquationsF.C.NelsonProfessorofMechanicalEngineeringTuftsUniversityMedford,MA02155USAFrederick.nelson@tufts.eduDr.FrederickNelsonisProfessorofMechanicalEngineeringatTuftsUniversityinMedford,Massachusetts
2、,USA.HeisamemberoftheBoardofDirectorsoftheVibrationInstituteandafellowoftheAmericanSocietyofMechanicalEngineers,AcousticalSocietyofAmerica,andtheAmericanAssociationfortheAdvancementofScience.HehasbeenaVisitingProfessorattheInstituteforSoundandVibrationResearchandtheInstitut
3、NationaldesSciencesAppliqueesdeLyon.ABSTRACTTheanalysisofthelateralandtorsionalmotionofspinningrotorsisrepletewithapplicationsofNewton'sandEuler'sequations.Sometimestheintricaciesoftheseequationsovershadowtheirsimplerphysicalmeaning.Thispaperattemptstocompensateforthisbyexp
4、lainingthedynamicbehaviorofspinningrotorswithoutwritinganyequations.1.INTRODUCTIONTheJeffcottrotormodelisobviouslyanoversimplificationofreal-worldrotorsbutitneverthelessThefirstsuccessfulrotormodelwasproposedbyassistsanunderstandingofmanyfeaturesofreal-worldrotorFöpplin1895
5、.Itconsistedofasinglediskcentrallylocatedbehavior,includingcriticalspeeds,gyroscopicaction,andonacircularshaft,withoutdamping.Itdemonstratedthatthedestabilizingeffectofinternaldamping.Thefullrichnesssupercriticaloperationwasstable.Unfortunately,Föpplofthemodelisdemonstrated
6、inthebookbyKrämer[2].publishedhisworkinaGermancivilengineeringjournal,whichwaslittleread,ifatall,bytherotordynamics2.NATURALWHIRLING(PRECESSIONAL)communityofhisday.FREQUENCIESANDMODESIn1919Jeffcottconceivedthesamemodel,thisThedynamicsofarotorarenotexactlythesametimewithdamp
7、ing,andpublishedhisworkinawidelyreadasthedynamicsofaspring-masssystem.ThereferenceEnglishjournal.Asaresult,intheUKandtheUSAasinglestateofthelatterisstationarywhilethatoftheformerisdiskrotoriscalledaJeffcottrotor.Overtimemanyvariationsrotational.Nevertheless,theysharetheexis
8、tenceofnaturaloftheJeffcottrotorhavebeenstudiedbutitsmostfrequentfrequenciesandnat