Basic Dynamic Analysis User's Guide - Siemens

1 SIEMENSSIEMENSSIEMENSB asicDynamicAnalysisUser'sGuideContentsPr oprietary& , , ' (SOL103).. ' (SOLs108and111).. (SOL108).. (SOL111).. (SOLs109and112).. (SOL109).. ' (SOL112).. ' (SOL107).. (SOL129)..12-6 BasicDynamicAnalysisUser' (SOL200).. ' MODES,FREQUENCIES, 'sGuide9 ContentsProprietary&RestrictedRightsNoti ce normalmodesanalysis transientresponseanalysis frequencyresponseanalysis ,responsespectrumanalysis,randomresponse Analysis ,complexeigenvalueanalysis,nonli nearanalysis,controlsystems,fluid-struct urecouplingandtheLagrangeMultiplierMetho d,seetheNXNastranAdvancedDynamicAnalysis user 'sGuide1-1 Chapter2:FundamentalsofDynamicAnalysis Overview EquationsofMotion DynamicAnalysisProcess DynamicAnalysisTypesBasicDynamicAnalysis user 'sGuide2-1 Chapter2 , ,becausethereareseveraltypesofdynamicana lyses,eachwithadifferentmathematicalform , : Containsimportantinformationonnotationan dterminologyusedthroughouttherestofthebo ok.

2 Introducestheequationsofmotionforasingle degree-of-freedomdynamicsystem(seeEquati onsofMotion). Illustratesthedynamicanalysisprocess(see DynamicAnalysisProcess). Characterizesthetypesofdynamicanalysesde scribedinthisguide( : Dynamicloadsareappliedasafunctionoftime. Thistime-varyingloadapplicationinducesti me-varyingresponse(displacements,velocit ies,accelerations,forces,andstresses). ,respectively, 'sGuideChapter2 ,accelerationistherateofchangeoftheveloc itywithrespecttotime, (SDOF)system(seeFigure2-1).InanSDOF system,thetime-varyingdisplacementofthes tructureisdefinedbyonecomponentofmotionu (t). (inertia)b=damping(energydissipation)k=s tiffness(restoringforce)p=appliedforceu= displacementofmass =velocityofmass = (SDOF) ; (andoftendesirable) ,energydissipation(damper),resistance(sp ring), , ,whichdefinestheequilibriumconditionofth esystemateachpointintime,isrepresentedas BasicDynamicAnalysisUser'sGuide2-3 FundamentalsofDynamicAnalysisChapter2 , , ,typicallyheat, (t).)

3 AppliedLoadTheappliedloadp(t) ( ,anearthquakeisthesameearthquakewhetheri tisappliedtoahouse,officebuilding,orbrid ge), ,velocities,accelerations,and/orstresses allasafunctionoftime ( ,noappliedload).Ifdampingisneglected, 'sGuideChapter2:FundamentalsofDynamicAna lysisFundamentalsofDynamicAnalysisFreeVi brationAnalysisInundampedfreevibrationan alysis, (t) , natural , , ,commonlycyclespersecond(cps),whichismor ecommonlyknownasHertz(Hz).Thischaracteri sticindicatesthenumberofsineorcosineresp onsewavesthatoccurinagiventimeperiod(typ icallyonesecond).Thereciprocalofthenatur alfrequencyistermedtheperiodofresponseTn givenbyBasicDynamicAnalysisUser'sGuide2- 5 FundamentalsofDynamicAnalysisChapter2 , (t=0)andtheinitialvelocityofthesystemare known,AandBareevaluatedbysubstitutingthe irvaluesintothesolutionoftheequationford isplacementanditsfirstderivative(velocit y), , , UndampedFreeVibrationsIfdampingisinclude d, ,theequationofmotionbecomes2-6 BasicDynamicAnalysisUser'sGuideChapter2 Criticallydamped Overdamped , , > <.

4 BasicDynamicAnalysisUser'sGuide2-7 FundamentalsofDynamicAnalysisChapter2 , , ,moststructureshavecriticaldampingvalues inthe0to10%range,withvaluesof1to5% , , ,solutionsforundampednaturalfrequenciesa remostcommonlyusedtodeterminethedynamicc haracteristicsofthesystem(see RealEigenvalueAnalysis ).However, (seeFrequencyResponseAnalysisand TransientResponseAnalysis ). , 'sGuideChapter2 ,thesimplestloadingissimpleharmonic(sinu soidal) , .Thisloadingfrequencyisentirelyindepende ntofthestructuralnaturalfrequency n, :A=B=Again, ,iftheamplitudeofthesinusoidalloadingisa ppliedasastaticload, ,toobtainthesteadystatesolution, 'sGuide2-9 FundamentalsofDynamicAnalysisChapter2:Fu ndamentalsofDynamicAnalysisiscalledthedy namicamplification(load) ( ,thepeakdisplacementoccursatthetimeofpea kloading).

5 Astheappliedloadingfrequencybecomesappro ximatelyequaltothestructuralnaturalfrequ ency,theratio / ,thisconditionresultsinaninfinite(orunde fined) ,asthisconditionisreached, ,theequationofmotionbecomes2-10 BasicDynamicAnalysisUser'sGuideChapter2 , , ,theloadingandresponseareseparatedbyanin tervaloftimemeasuredintermsofaphaseangle iscalledthephaselead, asthephaselag, ,changethesignof ,theappliedloadfrequency, / nismuchlessthan1, / nismuchgreaterthan1,thedynamicamplificat ionfactorapproacheszero, ,thestructuredoesnotrespondtoBasicDynami cAnalysisUser'sGuide2-11 FundamentalsofDynamicAnalysisChapter2 ,anymeasurabledisplacementresponsewillbe 180degreesoutofphasewiththeloading( ,thedisplacementresponsewillhavetheoppos itesignfromtheforce).

6 Finallyif / n=1, ,themagnificationfactoris1/(2 ), ,themoregeneralformsofloading(impulsesan dgeneraltransientloading) ,knownasnumericalintegration, TransientResponseAnalysis . , ( ,normalmodes,transientresponse,frequency response,etc.).Thisenvironmentalsoindica testhedominantbehaviorthatmustbeincluded intheanalysis( ,contact,largedisplacements,etc.). 'sGuideChapter2 , ,justasimportantly,thenatureofthedynamic loading(typeandfrequency)andanyinteracti ngmedia(fluids,adjacentstructures,etc.). Atthispoint,thefirststepinmanydynamicana lysesisamodalanalysistodeterminethestruc ture snaturalfrequenciesandmodeshapes(see RealEigenvalueAnalysis ). ,indesigningthesupportingstructureforaro tatingfan,thedesignrequirementsmayrequir ethatthenaturalfrequencyofthesupportings tructurehaveanaturalfrequencyeitherlesst han85%orgreaterthan110% , (loading).

7 'sGuide2-13 FundamentalsofDynamicAnalysisChapter2 (es) : Realeigenvalueanalysis(undampedfreevibra tions). Linearfrequencyresponseanalysis(steady-s tateresponseoflinearstructurestoloadstha tvaryasafunctionoffrequency). Lineartransientresponseanalysis(response oflinearstructurestoloadsthatvaryasafunc tionoftime).Additionally,NXNastranallows youtoperformanumberoftypeofadvanceddynam icsanalysis,suchasshock/responsespectrum Analysis ,randomresponseanalysis,designse nsitivity,designoptimization,aeroelastic ity, , RealEigenvalueAnalysis . ,theloadingisasinewaveforwhichthefrequen cy,amplitude, ,butisexplicitlydefined( ,known) (transient) TransientResponseAnalysis . AdvancedDynamicAnalysisCapabilities andwillbedescribedfullyintheNXNastranAdv ancedDynamicAnalysisUser 'sGuideChapter2:FundamentalsofDynamicAna lysisChapter3:FiniteElementInputData Overview MassInput DampingInput UnitsinDynamicAnalysis DirectMatrixInputBasicDynamicAnalysisUse r'sGuide3-1 Chapter3 , ,youneedtoobtainstressdata, ,withadynamicanalysis, MassInput describesmassinput,and DampingInput ,youmustensuretheirconsistency(andaccura cy).

8 UnitsinDynamicAnalysis describesthecommonvariablesandunitsfordy namicanalysis. DirectMatrixInput (CBAR,CQUAD4,etc.)inNXNastran,whenconcen tratedmasselementsareentered, , , ,CBEAM,CROD, ,themassmatrixformulationiscontrolledwit hPARAM, (default), ,COUPMASS,1, , CoupledMassMatrixTerms inChapter2oftheAdvancedDynamicAnalysisUs er' 'sGuideChapter3 , :BasicDynamicAnalysisUser'sGuide3-3 FiniteElementInputDataChapter3:FiniteEle mentInputDataCRODE lementStiffnessMatrixTheCROD element sstiffnessmatrix[K] (uncoupled)translationalandrotationalbeh aviorfortheCROD element, 'sGuideChapter3 , , , (Figure3-1).Theexactquarter-wavenaturalf requencyforthefirstaxialmodeisBasicDynam icAnalysisUser'sGuide3-5 FiniteElementInputDataChapter3:FiniteEle mentInputDataUsingthelumpedmassformulati onfortheCROD element,thefirstfrequencyispredictedtobe whichunderestimatesthefrequencyby10%.

9 Usingaclassicalconsistentmassapproach,th epredictedfrequencyisoverestimatedby10%. UsingthecoupledmassformulationinNXNastra n, ,asthemodel smeshbecomesfiner, 'sGuideChapter3 , ,CBEAMC oupledMassTheCBAR elementcoupledmassmatrixisidenticaltothe classicalconsistentmassformulationexcept fortwoterms:(1)themassintheaxialdirectio nistheaverageofthelumpedandclassicalcons istentmasses,asexplainedfortheCROD element;and(2) :(1)themassintheaxialdirectionisthelumpe dmass;and(2) ,loads,materialproperties, , , :=massormassdensity=accelerationofgravit y=weightorweightdensityTheparameterPARAM ,WTMASS, ,thedefaultvalueforWTMASS assumesthatmass(andmassdensity)isentered ,insteadofweight(andweightdensity). Basic DynamicAnalysisUser'sGuide3-7 FiniteElementInputDataChapter3:FiniteEle mentInputDataWhenusingEnglishunitsifthew eightdensityofsteelisenteredasRHO= ,usingPARAM,WTMASS, ,therefore, ,thenusingPARAM,WTMASS, ,therefore,becomes8160 ,WTMASS isusedonceperrun,anditmultipliesallweigh t/massinput(includingCMASSi,CONMi,andnon structuralmassinput).

10 Therefore,donotmixinputtype;useallmass(a ndmassdensity)inputorallweight(orweightd ensity) ,WTMASS doesnotaffectdirectinputmatricesM2 GGorM2PP(see DirectMatrixInput ).PARAM,CM2canbeusedtoscaleM2GG; ,CM1issimilartoPARAM,WTMASS sinceCM1scalesallweight/massinput(except forM2 GGandM2PP), ,PARAM,CM1isusedinadditiontoPARAM, (mass/unitvolume).Todeterminethetotalmas softheelement,themassdensityismultiplied bytheelementvolume(determinedfromthegeom etryandphysicalproperties).ForaMAT1entry , :12345678910$ ,CONM2, , , ,roofingmaterial, (PBAR,forexample). Viscouseffects(dashpot,shockabsorber) Externalfriction(slippageinstructuraljoi nts) Internalfriction(characteristicofthemate rialtype)3-8 BasicDynamicAnalysisUser'sGuideChapter3: FiniteElementInputDataFiniteElementInput Data Structuralnonlinearities(plasticity,gaps )Becausetheseeffectsaredifficulttoquanti fy, , (s) :b=viscousdampingcoefficient=.