Dynamic Substructures, Volume 4: Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics 2022

133 Pages·2022·11.557 MB·English

by  Matthew Allen, Walter D'Ambrogio, Dan Roettgen

Conference Proceedings of the Society for Experimental Mechanics Series
Matthew Allen
Walter D’Ambrogio
Dan Roettgen   Editors
Dynamic
Substructures,
Volume 4
Proceedings of the 40th IMAC, A Conference and
Exposition on Structural Dynamics 2022
Conference Proceedings of the Society for Experimental Mechanics
Series
SeriesEditor
KristinB.Zimmerman
SocietyforExperimentalMechanics,Inc.,
Bethel,CT,USA
TheConferenceProceedingsoftheSocietyforExperimentalMechanicsSeriespresentsearlyfindingsandcasestudiesfrom
a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics.
SeriesvolumesfollowtheprincipletracksorfocustopicsfeaturedineachoftheSociety’stwoannualconferences:IMAC,
AConferenceandExpositiononStructuralDynamics,andtheSociety’sAnnualConference&Expositionandwilladdress
criticalareasofinteresttoresearchersanddesignengineersworkinginallareasofStructuralDynamics,SolidMechanics
andMaterialsResearch.
Matthew Allen • Walter D’Ambrogio • Dan Roettgen
Editors
Dynamic Substructures, Volume 4
Proceedings of the 40th IMAC, A Conference and Exposition on
Structural Dynamics 2022
Editors
MatthewAllen WalterD’Ambrogio
BrighamYoungUniversity DIIIE
Provo,UT,USA UniversityofL’Aquila
L’AQUILA,L’Aquila,Italy
DanRoettgen
SandiaNationalLaboratories
Albuquerque,NM,USA
ISSN2191-5644 ISSN2191-5652 (electronic)
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries
ISBN978-3-031-04093-1 ISBN978-3-031-04094-8 (eBook)
https://doi.org/10.1007/978-3-031-04094-8
©TheSocietyforExperimentalMechanics,Inc.2023
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Preface
DynamicSubstructuresrepresentsoneofninevolumesoftechnicalpaperspresentedatthe40thIMAC,AConferenceand
ExpositiononStructuralDynamics,organizedbytheSocietyforExperimentalMechanics,andheldFebruary7–10,2022.
The full proceedings also include volumes titled Nonlinear Structures & Systems; Dynamics of Civil Structures; Model
Validation and Uncertainty Quantification; Special Topics in Structural Dynamics & Experimental Techniques; Rotating
Machinery, Optical Methods & Scanning LDV Methods; Sensors and Instrumentation, Aircraft/Aerospace and Dynamic
EnvironmentsTesting;TopicsinModalAnalysis&ParameterIdentification;andDataScienceinEngineering.
Eachcollectionpresentsearlyfindingsfromexperimentalandcomputationalinvestigationsonanimportantareawithin
structuraldynamics.Coupledstructuresor,substructuring,isoneoftheseareas.
Substructuringisageneralparadigminengineeringdynamicswhereacomplicatedsystemisanalyzedbyconsideringthe
dynamicinteractionsbetweensubcomponents.Innumericalsimulations,substructuringallowsonetoreducethecomplexity
of parts of the system in order to construct a computationally efficient model of the assembled system. A subcomponent
model can also be derived experimentally, allowing one to predict the dynamic behavior of an assembly by combining
experimentally and/or analytically derived models. This can be advantageous for subcomponents that are expensive or
difficult to model analytically. Substructuring can also be used to couple numerical simulation with real-time testing of
components.Suchapproachesareknownashardware-in-the-looporhybridtesting.
Whetherexperimentalornumerical,allsubstructuringapproacheshaveacommonbasis,namelytheequilibriumofthe
substructures under the action of the applied and interface forces and the compatibility of displacements at the interfaces
of the subcomponents. Experimental substructuring requires special care in the way the measurements are obtained and
processedinordertoassurethatmeasurementinaccuraciesandnoisedonotinvalidatetheresults.Innumericalapproaches,
the fundamental questis theefficient computation of reduced order models describing thesubstructure’s dynamic motion.
Forhardware-in-the-loopapplications,difficultiesincludethefastcomputationofthenumericalcomponentsandtheproper
sensingandactuationofthehardwarecomponent.Recentadvancesinexperimentaltechniques,sensor/actuatortechnologies,
novel numerical methods, and parallel computing have rekindled interest in substructuring in recent years leading to new
insightsandimprovedexperimentalandanalyticaltechniques.
Theorganizerswouldliketothanktheauthors,presenters,sessionorganizers,andsessionchairsfortheirparticipationin
thistrack.
Provo,UT,USA MatthewAllen
L’Aquila,Italy WalterD’Ambrogio
Albuquerque,NM,USA DanRoettgen
v
Contents
1 UncertaintyinPowerFlowDuetoMeasurementErrorsinVirtualPointTransformationfor
Frequency-BasedSubstructuring............................................................................ 1
JonYoungandKyleMyers
2 Using Flight Test Measurements on a Low-Fidelity Component to Predict Response
onaHigh-FidelityComponent............................................................................... 11
RandallL.Mayes
3 RoadNoiseNVHPart2:ExploringtheCapabilitiesoftheTPAFrameworkwithInterface
Forces ........................................................................................................... 19
JulieM.Harvie,MaartenV.vanderSeijs,DavidP.Song,andMunhwanCho
4 Real-TimeHybridSubstructuringforShockApplicationsConsideringEffectiveActuator
Control.......................................................................................................... 29
ChristinaInsam,MichaelJ.Harris,MatthewR.Stevens,andRichardE.Christenson
5 HrishikeshS.Gosavi,PhanisriP.Pratapa,andVijayaV.N.SriramMalladi .......................... 41
HrishikeshS.Gosavi,PhanisriP.Pratapa,andVijayaV.N.SriramMalladi
6 AnAssessmentontheEfficiencyofDifferentReductionTechniquesBasedonSubstructuring
forBladedDiskSystemswithShrouds...................................................................... 49
EhsanNaghizadehandEnderCigeroglu
7 SandorBeregi,DavidA.W.Barton,DjamelRezgui,andSimonA.Neild.............................. 59
SandorBeregi,DavidA.W.Barton,DjamelRezgui,andSimonA.Neild
8 AccuracyofNonlinearSubstructuringTechniqueintheModalDomain............................... 63
JacopoBrunetti,WalterD’Ambrogio,AnnalisaFregolent,andFrancescoLatini
9 QuantificationofBiasErrorsInfluenceinFrequencyBasedSubstructuringUsingSensitivity
Analysis......................................................................................................... 71
GregorCˇepon,DomenOcepek,JureKorbar,TomažBregar,andMihaBoltežar
10 Real-TimeandPseudo-DynamicHybridSimulationMethods:ATutorial............................. 75
Oh-SungKwonandVasilisDertimanis
11 IdentificationofBoltedJointPropertiesThroughSubstructureDecoupling........................... 85
JacopoBrunetti,WalterD’Ambrogio,MatteoDiManno,AnnalisaFregolent,andFrancescoLatini
12 ParametricAnalysisoftheExpansionProcessBasedonSystemEquivalentModelMixing ......... 97
MihaKodricˇ,TomažBregar,GregorCˇepon,andMihaBoltežar
13 Real-TimeHybridSimulationStudyofaPhysicalDuffingAbsorberAttachedtoaVirtual
NonlinearStructure........................................................................................... 101
A.MarioPuhweinandMarkusJ.Hochrainer
vii
viii Contents
14 SystemEquivalentModelMixing(SEMM):AModalDomainFormulation........................... 111
MihaPogacˇar,DomenOcepek,GregorCˇepon,andMihaBoltežar
15 HybridTestingofaCantileverBeamwithTwoControlledDegreesofFreedom ...................... 115
AlessandraVizzaccaro,SandorBeregi,DavidBarton,andSimonNeild
16 ExperimentalSubstructuringoftheDynamicSubstructuresRound-RobinTestbed ................. 119
D.Roettgen,G.Lopp,A.Jaramillo,andB.Moldenhauer
17 FeasibilityofConfiguration-DependentSubstructureDecoupling ...................................... 125
JacopoBrunetti,WalterD’Ambrogio,andAnnalisaFregolent
Chapter 1
Uncertainty in Power Flow Due to Measurement Errors
in Virtual Point Transformation for Frequency-Based
Substructuring
JonYoungandKyleMyers
Abstract Experimentalsubstructuringbymeansofvirtualpointtransformation(VPT)canbeutilizedtoimplicitlyaccount
for rotational degrees of freedom (DOFs) at the coupling boundary of a given substructure. Measured frequency response
functions (FRFs) are cast onto a “virtual” node containing three translational and three rotational DOFs via a projection
matrix,whichisdeterminedbygeometricrelationsbetweenimpactandresponselocationsonthestructure.Inthisstudy,the
uncertainty of power flow due to measurement errors in the projection matrix and FRFs is quantified by means of Monte-
Carlosimulation.Thisisperformedonanumericalmodeloftwobeamstructuresandisthencomparedtoexperimentally
obtaineddatausinganimpactmodaltest.Upperandlowerboundsonthebroadbandpowerflowarecreatedusingthesedata.
Itisshownthatcloselyspacemodesleadtohighvariabilityinthecalculationofpowerflownearresonanceevenforsmall
measurementerrors.Metricsforanalyzingthequalityofthevirtualpointtransformationarediscussed,aswell.Thisworkis
beneficialtounderstandinghowexperimentalerrorsmanifestinthecalculationofpowerflowbetweencoupledstructures.
Keywords Powerflow · Dynamicsubstructuring · Virtualpointtransformation · Monte-Carlo · Uncertainty
quantification
1.1 Introduction
Frequency-based substructuring has been thoroughly developed over the past several decades for the steady-state analysis
ofnumericalstructuralmodels.Itsapplicationtoexperimentaldata,however,leadstoseveraldifficultieswhich,ingeneral,
make experimental substructuring a more cumbersome means of predicting the dynamics of complex structures [1]. A set
of frequency response functions (FRFs) are used to define the dynamic properties of the structures of interest when they
are uncoupled from each other [2–4]. These FRFs are then assembled by enforcing displacement compatibility and force
equilibriumontheircouplinginterfaces,andtheresultingFRFspredictthefrequencyresponseoftheassembledstructures.
These FRFs are generally obtained using modal impact testing, but shakers or laser vibrometers can also be used [5]. Of
course,measurementerrorsduetonoiseanduncertaintyintheexactpositionandorientationofaccelerometersandimpacts
are inevitable, but the measurements of rotational degrees of freedom (DOFs) which contain necessary information for
proper substructure coupling are generally impossible to measure. Moreover, these errors are drastically amplified during
substructureassemblyduetotheinversionoftheinterfaceFRFsandfurthermagnifiedifpowerflowbetweensubstructures
iscalculatedduetoitsquadraticform.
To account for the rotational DOFs on the substructure interfaces, the virtual point transformation (VPT) has been
developed and successfully used to couple experimental substructures [6–8]. It implements a least-squares residual
minimization to project the dynamics measured by accelerometers onto a virtual point which contains three translational
and three rotational DOFs. The projection is done using only the geometric relations between the virtual point and the
interface impact and response measurements. The primary assumption is that the interface being modelled with a virtual
pointbehavesrigidlyinthefrequencyrangebeinganalyzed.Thatis,thereisnolocalflexibledeformationoftheinterface.
J.Young((cid:2))
DepartmentofMechanicalEngineering,PennsylvaniaStateUniversity,StateCollege,PA,USA
K.Myers
StructuralAcousticsDepartment,PennStateAppliedResearchLaboratory,StateCollege,PA,USA
e-mail:[email protected]
©TheSocietyforExperimentalMechanics,Inc.2023 1
M.Allenetal.(eds.),DynamicSubstructures,Volume4,ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries,
https://doi.org/10.1007/978-3-031-04094-8_1
2 J.YoungandK.Myers
Metricssuchasoverallsensorandimpactconsistencyhavebeendevelopedtoquantifythisassumptionforagivenvirtual
point[9].
TheVPThasbeendevelopedtobeappliedtotheLagrangeMultiplierFrequency-BasedSubstructuring(LMFBS)method
[3].Itisknownasadualsubstructureassemblymethodbecauseinadditiontothedisplacementsoftheassembledstructure
beingsolvedfor,thecouplingforcebetweensubstructureinterfacesisexplicitlysolvedfor.Thisisparticularlyusefulwhen
calculatingpowerflowbecauseitcanbeexpressedintermsofthecouplinginterfacemobilityandthecouplingforcebetween
substructures.PowerflowbetweensubstructuresthroughflexiblejointshasbeenstudiedinthepastusingtheLMFBSasthe
methodofassembly[10].However,thisstudyfocusedoncorrectinganumericalmodelwithaflexibleelasticanddissipative
interfacesotheresponseoftheassemblywouldbettermatchexperimentaldata.Thistypeofinterfacemodellingwillnotbe
usedinthiswork,andinsteadarigidconnectionisassumed.
Since the VPT requires the projection of physical measurements onto a virtual node near the coupling interface of a
substructure, it would be beneficial to know how measurement errors in this projection propagate through the calculation
of a response quantity. In this study, power flow from a source to receiver beam structure is the response quantity of
interestbecauseitisasinglescalarmeasureoftheresponseoftheassembledstructures.Measurementuncertaintyinboth
the projection matrix and FRFs is tracked through the substructure assembly process and calculation of power flow, and
distributions of power flow and overall sensor consistency are estimated using the results from a Monte-Carlo simulation.
Additionally,differentrangesofmaximumuncertaintyintheprojectionmatrixmeasurementsarestudiedtounderstandhow
variability in power flow changes with respect to the amount of uncertainty in the VPT. These simulated results are then
comparedtosomepreliminaryexperimentaldata.
1.2 VirtualPointTransformation
TheVPTprojectsmeasureddisplacementsandforcesontoavirtualpointwiththreetranslationalandthreerotationalDOFs.
Theprojectionoftheresponsemeasuredbyaccelerometerkontovirtualpointvisgivenby
uk =Rkvqv +μk (1.1)
u
where
⎡ ⎤⎡ ⎤
ek ek ek 100 0 rk −rk
⎢ x,X x,Y x,Z⎥ Z Y
Rkv =⎣ek ek ek ⎦⎣010 −rk 0 rk ⎦ (1.2)
u y,X y,Y y,Z Z X
ek ek ek 001 rk −rk 0
z,X z,Y z,Z Y X
is the displacement projection matrix. In previous literature, this matrix is said to contain the interface deformation
modes. The vector uk are the physical displacements measured by accelerometer k, and the vector qv are the virtual point
displacementsofvirtualpointv.ThisvectorcontainsthreetranslationalandthreerotationalDOFs.SincetheVPTassumesa
locallyrigidinterface,thevectorμk containstheresidualflexiblemotionoftheinterfacemeasuredbyaccelerometerk.The
leftmatrixinEq.1.2correspondstotheorientationoftheaccelerometerinthevirtualpointcoordinatesystem,andtheright
matrixcontainstheprojectioninformationforthetranslationalandrotationalDOFsofthevirtualpoint.Asimilarprojection
isperformedfortheinterfaceforcesappliedtothestructure
(cid:8) (cid:8)
mv =Rvh(cid:8)fh(cid:8) (1.3)
f
where
⎡ ⎤
(cid:9) (cid:10) 100 0 rZh −rYh
Rhv = eh eh eh ⎣010 −rh 0 rh ⎦ (1.4)
f X Y Z Z X
001 rh −rh 0
Y X
is the force projection matrix. Note that the transpose of the force projection matrix is given in Eq. 1.3 due to the virtual
pointmomentsnotbeingabletobeuniquelydefinedgivenonlyimpactforcemagnitude(cid:2)fh(cid:2)andorientation.(cid:9)Here,mv ar(cid:10)e
thevirtualforcesonvirtualpointv,andfhistheforcevectorofinterfaceimpacthwhosedirectionisgivenby eh eh eh .
X Y Z