Fundamentals of Vibration

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1、PrintthispageFundamentalsofVibrationVibrationandvibrationisolationarebothintimatelyconnectedwiththephenomenonofresonanceandsimpleharmonicmotion.SimpleHarmonicMotionAsimpleexampleofharmonicmotionisamassconnectedtoaflexiblecantileveredbeam.Externalforce,eitherfromaone-timeimpulseorfromaperiodicforce

2、suchasvibration,willcausethesystemtoresonateasthespringalternatelystoresandimpartsenergytothemovingmass.Massoncantileveredbeamresonatingundertheinfluenceofanexternalforce.NaturalFrequencyThenaturalfrequency,asthenameimplies,isthefrequencyatwhichthesystemresonates.Intheexampleofthemassandbeam,thena

3、turalfrequencyisdeterminedbytwofactors:theamountofmass,andthestiffnessofthebeam,whichactsasaspring.Alowermassand/orastifferbeamincreasethenaturalfrequency;ahighermassand/orasofterbeamlowerthenaturalfrequency.(Left)Alowermassincreasesnaturalfrequency.(Right)Ahighermasslowersnaturalfrequency.(Left)A

4、stifferspringincreasesnaturalfrequency.(Right)Amorecompliant(”softer”)springdecreasesnaturalfrequency.Anothersimpleexampleofnaturalfrequencyisatuningfork,whichisdesignedtovibrateataparticularnaturalfrequency.Forexample,atuningforkforthemusicalnote“A”vibratesatafrequencyof440Hz.Justasthenaturalfreq

5、uencyofthecantileveredbeamcanbechangedwithadifferentspringrateorachangeinthemass,thenaturalfrequencyofthetuningforkcanbealteredbyaddingorreducingmassofthetwotinesand/orbymakingthetineslongerorshorter.Atuningforkvibratesatanaturalfrequencydeterminedbythelengthandmassofthetines.DampingInthecantileve

6、redbeamandtuningforkmodels,weconsideredundampedsystemsinwhichthereisnomechanismtodissipatemechanicalenergy.Withoutdamping,thesesystemswillvibrateforquitealongperiodoftime—atleastseveralseconds—beforecomingtorest.Dampingdissipatesmechanicalenergyfromthesystemandattenuatesvibrationsmorequickly.Forex

7、ample,whenthetuningfork’stipsareimmersedinwater,thevibrationsarealmostinstantlyattenuated.Similarly,whenafingertouchestheresonatingmass-beamsystemlightly,thisdampingactionalsorapidlydissipatesthevibrationalenergy