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1、8434_Harris_07_b.qxd09/20/200111:24AMPage7.1CHAPTER7VIBRATIONOFSYSTEMSHAVINGDISTRIBUTEDMASSANDELASTICITYWilliamF.StokeyINTRODUCTIONPrecedingchaptersconsiderthevibrationoflumpedparametersystems;i.e.,systemsthatareidealizedasrigidmassesjoinedbymasslessspr
2、ingsanddampers.Manyengineeringproblemsaresolvedbyanalysesbasedonidealmodelsofanactualsys-tem,givinganswersthatareusefulthoughapproximate.Ingeneral,moreaccurateresultsareobtainedbyincreasingthenumberofmasses,springs,anddampers;i.e.,byincreasingthenumbero
3、fdegrees-of-freedom.Asthenumberofdegrees-of-freedomisincreasedwithoutlimit,theconceptofthesystemwithdistributedmassandelasticityisformed.Thischapterdiscussesthefreeandforcedvibrationofsuchsystems.Typesofsystemsincluderodsvibratingintorsionalmodesandinte
4、nsion-compressionmodes,andbeamsandplatesvibratinginflexuralmodes.Particularattentionisgiventothecalculationofthenaturalfrequenciesofsuchsystemsforfurtheruseinotheranalyses.Numerouschartsandtablesareincludedtodefineinreadilyavailableformthenaturalfrequen
5、ciesofsystemscommonlyencounteredinengineeringpractice.FREEVIBRATIONDegrees-of-Freedom.Systemsforwhichthemassandelasticpartsarelumpedarecharacterizedbyafinitenumberofdegrees-of-freedom.Inphysicalsystems,allelasticmembershavemass,andallmasseshavesomeelast
6、icity;thus,allrealsystemshavedistributedparameters.Inmakingananalysis,itisoftenassumedthatrealsys-temshavetheirparameterslumped.Forexample,intheanalysisofasystemconsist-ingofamassandaspring,itiscommonlyassumedthatthemassofthespringisnegligiblesothatitso
7、nlyeffectistoexertaforcebetweenthemassandthesupporttowhichthespringisattached,andthatthemassisperfectlyrigidsothatitdoesnot7.18434_Harris_07_b.qxd09/20/200111:24AMPage7.27.2CHAPTERSEVENdeformandexertanyelasticforce.Theeffectofthemassofthespringonthemoti
8、onofthesystemmaybeconsideredinanapproximateway,whilestillmaintainingtheassumptionofonedegree-of-freedom,byassumingthatthespringmovessothatthedeflectionofeachofitselementscanbedescribedbyasingleparameter.Acom-monlyusedassumptionis
