damping models for structural vibration

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1、DampingModelsforStructuralVibrationCambridgeUniversityEngineeringDepartmentAdissertationsubmittedtotheUniversityofCambridgefortheDegreeofDoctorofPhilosophybySondiponAdhikariTrinityCollege,CambridgeSeptember,2000iiTomyParentsivDeclarationThisdissertationdescribespartoftheresear

2、chperformedattheCambridgeUniversityEngineeringDepartmentbetweenOctober1997andSeptember2000.Itistheresultofmyownworkandincludesnothingwhichistheoutcomeofworkdoneincollaboration,exceptwherestated.Thedissertationcontainsapproximately63,000words,120figuresand160references.SondiponA

3、dhikariSeptember,2000vviDECLARATIONAbstractThisdissertationreportsasystematicstudyonanalysisandidentificationofmultipleparameterdampedmechanicalsystems.Theattentionisfocusedonviscouslyandnon-viscouslydampedmultipledegree-of-freedomlinearvibratingsystems.Thenon-viscousdampingmod

4、elissuchthatthedampingforcesdependonthepasthistoryofmotionviaconvolutionintegralsoversomekernelfunctions.Thefamiliarviscousdampingmodelisaspecialcaseofthisgenerallineardampingmodelwhenthekernelfunctionshavenomemory.Theconceptofproportionaldampingiscriticallyexaminedandageneral

5、izedformofproportionaldampingisproposed.Itisshownthattheproportionaldampingcanexistevenwhenthedampingmechanismisnon-viscous.Classicalmodalanalysisisextendedtodealwithgeneralnon-viscouslydampedmultipledegree-of-freedomlineardynamicsystems.Thenewmethodissimilartotheexistingmetho

6、dwithsomemodificationsduetonon-viscouseffectofthedampingmechanism.Theconceptof(complex)elasticmodesandnon-viscousmodeshavebeenintroducedandnumericalmethodsaresuggestedtoobtainthem.Itisfurthershownthatthesystemresponsecanbeobtainedexactlyintermsofthesemodes.Modeorthogonalityrela

7、tionships,knownforundampedorviscouslydampedsystems,havebeengeneralizedtonon-viscouslydampedsystems.Severalusefulresultswhichrelatethemodeswiththesystemmatricesaredeveloped.Thesetheoreticaldevelopmentsonnon-viscouslydampedsystems,inlinewithclassicalmodalanaly-sis,giveimpetustow

8、ardsunderstandingdampingmechanismsingeneralmechanicalsystems.