1 - Introduction to Mechanical Vibrations书

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1、IntroductiontoMechanicalVibrations1.1IntroductionAllmechanicalsystemscomposedofmass,stiffnessanddampingelementsexhibitvibratoryresponsewhensubjecttotime-varyingdisturbances.Thepredictionandcontrolofthesedisturbancesisfundamentaltothedesignandoperationofmechanicalequipmen

2、t.Inparticular,theuseofsecondary,activeinputstothesysteminordertomodifythesystemresponseinacontrollablewayisthetopicofthisbook.Theanalysisofcontrolledsystemsisfoundedonthesameanalyticalapproachesusedtostudythevibrationsofelasticstructures.Abriefreviewofthemainconceptsofv

3、ibrationanalysisandtheassociatedtechniquesofsolutionisnecessarytosetthefoundationforthefollowingchapters.Inthischapterwebeginbydefiningterminologyandthemathematicalmethodsfordescribingthelinearresponseofvibratingsystems.Theequationsofmotionandlinearbehaviourofsingle-degr

4、ee-of-freedomsystemsareoutlinedforbothfreeandforcedresponse.TheuseoftheLaplacetransformtosolvefortransientresponseisreviewed.Theextensiontomulti-degree-of-freedomsystemsandthentheuseoffiniteelementanalysisarebrieflyintroduced.Theseapproachesarevalidforlightlydampedstruct

5、uresorelementsthataresmallrelativetothewavelengthofmotion.FormoredetailthereaderisreferredtothetextsofThomson(1993),Meirovitch(1967)andInman(1994).1.2TerminologyThefollowingisabrieflistofthemainterminologyanddefinitionsusedinanalysingthevibratoryresponseofmechanicalsyste

6、ms.Mechanicalsystem.Amechanicalsystemiscomposedofdistributedelementswhichexhibitcharacteristicsofmass,elasticityanddamping.Degreesoffreedom.Thenumberofdegreesoffreedomofasystemisequaltothenumberofindependentcoordinatepositionsrequiredtocompletelydescribethemotionofthesys

7、tem.Systemresponse.Allmechanicalsystemsexhibitsomeformofvibratoryresponsewhenexcitedbyeitherinternalorexternalforces.Thismotionmaybeirregularormayrepeatitselfatregularintervals,inwhichcaseitiscalledperiodicmotion.Period.TheperiodTisthetimetakenforonecompletecycleofmotion

8、.2ACTIVECONTROLOFVIBRATIONHarmonicmotionisthesimplestformofperiodicmotionwherebytheactualorobservedmoti