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1、4ShockandImpactDynamics4.1IntroductionThischapterbeginswithbasicimpactdynamics.Itincludesimpacteffectsduetovehicle/traincollisions,aircraft/missiletargetinteractions,dropweightsandfree-fallingbodiesandmissilesonconcreteandsteeltargets.Anup-to-dateimpactsimulationisincludedfor
2、jetfluidsonsoilsandrocks.Briefnumericalandexperimentaldataaregivenonimpactsandcollisionsonwatersurfaces.Aspecialsectionisincludedonsnow/iceimpactandanalysisofshockresponseofceramics.4.2TheImpactorasaProjectileAnimpactorintheformofamissileisfirstgivenaninitialvelocityanditisthe
3、npossibletoassumethatitismovingundertheactionofitsownweight.Iftheinitialvelocityisnotvertical,themissilewillmoveinacurveanditsflightcanbeevaluatedintermsofhorizontalandverticalcomponentsofdisplacement,velocityandacceleration.SometypicalexamplesaregiveninTable4.1.4.2.1DirectIm
4、pulse/ImpactandMomentumAnimpulseisdefinedasaforcemultipliedbytime,suchthatF1(t)=Fdt,(4.1)whereF1(t)istheimpulse,Fistheforceandtisthetime.Themomentumofabodyistheproductofitsmassanditsvelocity:momentum=mv,(4.2)5204ShockandImpactDynamicsTable4.1.Projectilestatisticsygyyusinamis
5、slieumisslieuuxAAamgxaxOOucosa(a)y(b)Ox–horizontalmisslieOy–verticaluByhAaxxO(c)Figure(a)showsamissileprojectedatavelocityufromaposition0.At0,x,x˙andx¨areallzero.Theonlyforceontheflightisequaltomg.Hencey,theaccelerationintheverticaldirection,is−g.Thegeneralformsofthevelocitya
6、nddistanceequationsare:v=u+at,(1)12s=ut+at,2x˙=ucosα,y˙=usinα−gt(Fig.(b)),(2)12x=(ucosα)t,y=(usinα)t−gt,(3)2x¨=0,y=−g.(4)Byeliminationoftfrom(3),thetrajectoryequationiswritteninaparabolicformas222y=xtanα−(gxsecα/2u).(5)Thevelocityvofthemissileduringflightatanyinstantintimeisg
7、ivenby√22−1v=(˙x+˙y)withα=tan(˙y/x˙)(6)sincey/˙x˙=(dy/dt)/(dx/dt)=dy/dx.Thedirectionofthevelocityatanyinstantisalongthetangenttothepathforthatparticularinstant.Ifthemissileisprojectedfromtheaircraftatan4.2TheImpactorasaProjectile521Table4.1.(continued)anglebelowitslevelinord
8、ertohitthetargetatthegroundlevel(theaircraftlevelistreatedashorizontal),(5)
