Advanced Dynamic Analysis User's Guide - Siemens

1 SIEMENSSIEMENSSIEMENSA dvancedDynamicAnalysisUser'sGuideContent sProprietary& ,ExtraPoints, (NOLINi).. ' ' (SOL107)..5-9 ModalComplexEigenvalueAnalysis(SOL110).. (NLTRDM odule)..5-28 Two-PointMethod(NLTRD2 Module).. ,DEQATN, ' , ,ADAMS, ,ADAMS, (MDF) (HOU)..A-3 TheModifiedTridiagonalMethods(MHOU,AHOU) ..A-5 TheInversePowerMethod(SINV).. ' 'sGuide7 ContentsProprietary&RestrictedRightsNoti ce Overview MassModeling ModelingDampingEffects DMIGs,ExtraPoints,andTransferFunctions NonlinearLoadFunctions(NOLINi) DebuggingDynamicModelsAdvancedDynamicAna lysisUser'sGuide2-1 Chapter2 , , , , , (fourtimesmoreisneeded)isinsufficient,th esolutionwillspill, , , , , , , , 'sGuideChapter2 (CPUtime,databasesize,outputrequirements ) , ,constraints,andloadingfunctionsfordynam icsaredescribedintheNXNastranBasicDynami cAnalysisUser ,itmaycontaincontrolsystemterms,fluidcom pressibility, ,F,proportionaltoanaccelerationterm producesamasstermM, , { } (CG) (massperunitvolume)ofthestructuralmateri als,whichcomprisesthefiniteelement(RHOon theMATiBulkDataentries).

2 (NSMonthepropertyBulkDataentry). ,theoffsetofthecenterofmassfromthegridpo int, , 'sGuide2-3 DynamicModelingOptionsChapter2 (i=1,2,3,4) ,respectively,andMisthemasscoefficient,s pecifiedontheCMASS ientry(oronthePMASS entryifi=2or4).Inmostapplications, ,theentrygeneratestheinertiaforcef1= M 1, (see EnforcedMotionwithLoads ). ,WTMASS,V1 ,iftheft-lb-secsystemisused,andthemassin putunitispounds,thenV1=1 (exceptthosedefinedonDMIG entries;PARAM,CM2,V1maybeusedfortheseins tead). ,COUPMASS,1 , , , ,GRDPNT,V1 ,V1, ,COUPMASS, 'sGuideChapter2:DynamicModelingOptionsDy namicModelingOptionsThetotalkineticenerg yoftheelementisrepresentedbyshapefunctio ns,whichinturn, ,OMIT, , (DMIG),andtransferfunctions(TF).Anexampl eofacoupledscalarmassisillustratedinthee xamplebelow:Aspring,k,andtwomasses,m1and m2, ,whenmodelingfluidsorotherspecialconnect ions,theusermaywishtousethedifferenceind isplacements, u=u1 u2, ,V,andthekineticenergy,T, , 'sGuide2-5 DynamicModelingOptionsChapter2 [u]=[u1, u] ; ,k,isnowconnectedto u1+ u=0astheMPCequation, , :SpinningBodiesIftheentirestructureisspi nningataconstantangularvelocity, , ,,andforalocationvectorofapoint,,theabso lutevelocityvectorofthepoint,, ;thesecondtermisthecentripetalstiffness; thethirdtermistheCoriolisforce;thelastte rm,, 'sGuideChapter2 (Centrifugalstiffnessanddifferentialstif fnesstermsareofthesamemagnitude.)

3 , , :[Bc]= ![Kc]=thecentripetalstiffnessmatrix[Kd]= ,afrequencyresponse, n i n~P , ,thesystemisunstableif , , {u}aredisplacementsrelativetothemovingsy stemand{a0} [D]isamatrixwhosecolumnsdefinetherigidbo dymotionsofthestructure,thenforafreebody , 'sGuide2-7 DynamicModelingOptionsChapter2:DynamicMo delingOptionswhere[D] ,sincethefull-sizedvector,{ao},isarigidb odymotion,itmaybedefinedintermsofacceler ationsatasetofreferencecoordinates,{ar}, {ar}, , ,{u0},thetotalstructuralmotion,{uA}, {ug} ,wemayassumethatthe{u0} {}totherighthandsideitlooksalmostidentic altoagravityload:2-8 AdvancedDynamicAnalysisUser'sGuideChapte r2 , , ,seethe NXNastranBasicDynamicAnalysisUser sGuide .CaseControlLOADSET=20$ $RequestsDynamicLoad#200 BulkDataGRAV,386,, , $DefinesGravityLoadin-xdirectionLSEQ,20, 201,386$AssemblesGRAV loadvector$ ,200,201,etc.

4 $ , ,describedin EnforcedMotionwithLoads . , ,theinternalhysteresisthatoccursinmateri alssuchasrubber,frictioninjoints, ,structural,modal, 'sGuide2-9 DynamicModelingOptionsChapter2 , ,MATi,andontheparameter, , ,thematrixtermsareconvertedtoequivalentv iscousdamping; , ,K, ,theimaginarystiffness,G, ,intermsofthecomplexdisplacementsis2-10 AdvancedDynamicAnalysisUser'sGuideChapte r2 ,u0isnormallyacomplexvariablethatwewills ettoarealnumber, isthesteadystatefrequency,andeix=cos(x)+ sin(x).Ifastructuraldampingcoefficient,G ,isaddedtothestiffnessmatrix, , , , 'sGuide2-11 DynamicModelingOptionsChapter2:DynamicMo delingOptionsNotethattheelasticenergyter msaveragezeroovertheinterval, , (Hint:constructasimilartrajectorycurvean destimatethearea.)Themaindisadvantageofs tructuraldampingisthatcomplexnumbersmust beconvertedtorealnumbersintransientanaly sis; , , , , whendampingfactorsarespecifiedbyathirdpa rty , ,andaddedtoanydirectmatrixinputs, , , iistheundampedvibrationfrequency(equalto ), ,gi, ,g(f).

5 ,butitisproportionaltothestiffnessmatrix , ,b, 'sGuideChapter2:DynamicModelingOptionsDy namicModelingOptionsotherwords, ,gonaTABDMP1 BulkDataentry, (C/Cc)oramplificationqualityfactor(Q).If accuratetestresultsareavailable,theuserc anspecifydifferentdampingcoefficients,ob tainedfrommodaltests, , ,[B], [bi] , isthematrixofeigenvectors,and[Bv] [Bv]maywellbeduplicatedbytheeffectsinclu dedin[bi]sothat,ingeneral, ,thecompletedampingmatrixissimilar, ,thematrix[ ]T[Bv][ ] ,ortheequivalentcomplexstiffnessmatrix,i sgenerallycoupledsothattheefficientuncou pledmethodsofanalysiscannotbeusedwhen[Bv ] , ,Cc, , i, ,Qi,withthedefinitionAdvancedDynamicAnal ysisUser'sGuide2-13 DynamicModelingOptionsChapter2 , , (constantviscousdampingandequivalentstru cturaldamping) (SOL129). ,see NonlinearTransientResponseAnalysis.

6 ForbasicinformationontheNXNastrannonline arsolutions,seetheNXNastranHandbookforNo nlinearAnalysisortheNXNastranUser , , 'sGuideChapter2:DynamicModelingOptionsDy namicModelingOptionseffectsmustbemodeled withstructuraldampingparameters, ,definedwithparametersandmaterialbulkdat ainputs(theGEfieldontheMATientries), ,however, (andthereforemodaldamping) ,ExtraPoints,andTransferFunctionsIndynam icsmodeling,wefrequentlyneedtoincludespe cialnonfiniteelementeffectssuchasmechani caldevices,servomechanisms,smartstructur es, (EPOINT data)andnormalscalarpoints(SPOINT data) ,structuralelements,constraints, ,aswithscalarpoints, (see SetNotations ),theextrapointsetmergeswiththestructura ldegrees-of-freedomaccordingtothefollowi ngdiagram:AdvancedDynamicAnalysisUser'sG uide2-15 DynamicModelingOptionsChapter2:DynamicMo delingOptionsIndirectsolutions, , , 4,andflexiblemodes, , ,up, :2-16 AdvancedDynamicAnalysisUser'sGuideChapte r2:DynamicModelingOptionsDynamicModeling Options[ ph]=and ,P, ,K2PP, ,initialconditions, , (DMIG)dataiscoveredintheNXNastranUser sGuideandtheNXNastranBasicDynamicAnalysi sUser sGuide, ,B2PP=,andtheM2PP= ,thedirectinputmatricesaredefinedforthep -setofdegrees-of-freedomformass,damping, ,includingfluids,electricalcircuits, , (DMIG*) ,INPUTi, , 'sGuide2-17 DynamicModelingOptionsChapter2:DynamicMo delingOptionsAnexampleproblemthatusesDMI G dataforgeneratingfrictionforcesisgivenin ComplexEigensolutions.

7 TransferFunctionsTheNXNastrantransferfun ctions(TFinputs) ,uiaretheselectedinputdegrees-of-freedom , , [K].B1isaddedtothe[B]matrix,andB2isadded tothe[M]matrixonthediagonals, ,ui,A0i,A1i,andA2iareaddedtothecolumncor respondingtoui,andtherowcorrespondingtou d,ofthestiffness,damping,andmassmatrices , , , , (seethediscussionoftransferfunctionsbelo w). ,dynamicloads(DLOAD),andnonlinearfunctio ns(NOLINi) , , 'sGuideChapter2 ,thestructuraldisplacements,velocities, (includingfeedbackloops) ,velocity, ,Fjonastructuralpoint,uj,withatransferfu nction, , , ,ifapoint,ua, 'sGuide2-19 DynamicModelingOptionsChapter2 , ComplexEigensolutions .AlternateMethodIfthepolynomialisavailab leinfactoredform, ,G1(p) G2(p) G3(p).., ,theTFequationswillbeinthefollowingform: Forpolynomialsinthedenominatorofatransfe rfunction, ,considerthecontrolsystemshowninFigure2- 3, ,signalconditioners, ,whicharesensedbythecontrolsystem, (TFs) ,atpointu11, ,anextrapointisassignedtoeachofthenewvar iables,u4.

8 , ,expressedbyTFs1to6, ,u11, 'sGuideChapter2 AdvancedDynamicAnalysisUser'sGuide2-21 DynamicModelingOptionsChapter2 3 4 5 6 1u2u3 A B2u51 2u1 R3u61 3u10 14u7B0B1B2u4u5u6 CA0 DA0 EA0 CA1 DA1 EA15u81 4u11 k+ (u8= z),thefirstrategyro(u2=uy),andalumpedmas sarelocatedontherightend(GRID1).Thesecon drategyroisattachedtothenextpoint(GRID3) .Theactuatorisconnectedtotheleftend(GRID 11) ,kilograms,seconds,milliNewtons, (EPOINTs4,5,6,7,8,10) 'sGuideChapter2:DynamicModelingOptionsDy namicModelingOptionsIDADUG,TFANDEDIAG8 SOL107 TIME5 CENDTITLE=CONTROLSYSTEMEXAMPLEFORADUGSUB TITLE=TRANSFERFUNCTIONSANDEXTRAPOINTSLAB EL=COMPLEXMODESSPC=10 TFL=6 CMETHOD=200 SDISP=ALLBEGINBULK$EIGC,200,INV,MAX,,,,, ,+EIG1+EIG1, , , ,1200., ,10$$STRUCTUREISABOXBEAMPIVOTINGATTHECEN TERGRDSET,,,,,,,1345 GRID,1,, ,3,, ,14,, ,15,, ,11,, ,1,1,1,3,,, ,2,1,3,14,,, ,3,1,14,15,,, ,4,1,15,11,,, ,1,1,1000.

9 ,125+6,125+6,,250.+6 MAT1,1, +6,, , $OPTICALDEVICEONTHEENDCONM2,6,1,, ,,,,,+CNM2+CNM2, +5,, +5,,, +5$PIVOTONTHECENTERSPC,10,14,12$EXTRAPOI NTSAREVOLTAGESEPOINT,4,5,6,7,8,10$TRANSF ERFUNCTIONSINORDER$RATEGYROSPICKUPVELOCI TIESTF,6,4,, , ,,,,+TF101+TF101,1,2,, ,,,,,+TF102+TF102,3,2,, $ATTITUDESENSORMEASURESROTATIONRZTF,6,5, , , ,,,,+TF201+TF201,1,6, $INPUTSIGNAL,E10,ISFILTEREDTF,6,6,, , ,,,,+TF301+TF301,10,, $SIGNALCONDITIONERCOMBINESTHEVOLTAGESTF, 6,7,, , , ,,,+TF401+TF401,4,, , ,,,,,+TF402+TF402,5,, , ,,,,,+TF403+TF403,6,,100., $DISPLACEMENTFEEDBACKTOTHEACTUATORTF,6,8 ,, , ,,,,+TF501+TF501,11,2, $ACTUATORFORCESAREADDEDTOROWOFSTRUCTURAL MATRICESTF,6,11,2, ,,,,,+TF601+TF601,7,, +5,,,,,,+TF602+TF602,8,, +5$TEMPORARILYGROUNDPOINT10 WITHADIAGONALTERMTF,6,10,, (NOLINi)Thenonlinearloadfunctions(NOLINi ) ,joints, , 'sGuide2-23 DynamicModelingOptionsChapter2 , , , , :NONLINEAR, ,Ni,intermsofthedegrees-of-freedom,uj, (uj)F(uj)isaTABLED iinputNOLIN2Ni=SujukProductoftwovariable sNOLIN3Ni=S(uj)A,uj>0 AisaninputexponentNOLIN4Ni= S(uj)A,uj<0 SameexceptfornegativeuThevariables,u,may bedisplacementorvelocitycomponentsofgrid ,scalar, ,theconnecteddegrees-of-freedom,uianduj, etc.

10 ,mustremaininthesolutionset, , ,butunfortunately, {N}arethenonlinearforceswhicharedependen tonvariabledisplacements,{u},andvelociti es,{v}, ,theproperdefinitionofNwouldbeN= ,wewilldiscussthesimplestform, ,thesolutionis{un} ,the2-24 AdvancedDynamicAnalysisUser'sGuideChapte r2:DynamicModelingOptionsDynamicModeling Optionsaveragedvaluesofdisplacement,u,ve locity,v,acceleration,a,andload,P, ,thevectorsatstepn+ > , ,thenonlinearloadswouldbeconsistentwitht helineardisplacementsandloads, , ,Nn+1=N(un+1,vn+1) , ,whenuisrapidlychanging, 'sGuide2-25 DynamicModelingOptionsChapter2 , ,ifwedefinethefunctionasanequivalentspri ngwithN=ku,theintegrationequationforun+ ,wewillassumeauniformgrowthrate,r,whereu n=run 1andun+1= ,thesolutionwillpotentiallydiverge(rmayb ecomplex).