Special Topics in Structural Dynamics, Volume 6: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017

197 Pages·2017·15.055 MB·English

by  Nikolaos Dervilis (eds.)

Conference Proceedings of the Society for Experimental Mechanics Series
Nikolaos Dervilis Editor
Special Topics in
Structural Dynamics,
Volume 6
Proceedings of the 35th IMAC, A Conference and Exposition
on Structural Dynamics 2017
Conference Proceedings of the Society for Experimental Mechanics Series
SeriesEditor
Kristin B.Zimmerman,Ph.D.
SocietyforExperimental Mechanics,Inc.,
Bethel,CT,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/8922
Nikolaos Dervilis
Editor
Special Topics in Structural Dynamics,
Volume 6
Proceedings of the 35th IMAC, A Conference and Exposition
on Structural Dynamics 2017
123
Editor
NikolaosDervilis
UniversityofSheffield
Sheffield,UK
ISSN2191-5644 ISSN2191-5652 (electronic)
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries
ISBN978-3-319-53840-2 ISBN978-3-319-53841-9 (eBook)
DOI10.1007/978-3-319-53841-9
LibraryofCongressControlNumber:2017936948
©TheSocietyforExperimentalMechanics,Inc.2017
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Preface
Special Topics in Structural Dynamics represents one of ten volumes of technical papers presented at the 35th IMAC, A
Conference and Exposition on Structural Dynamics, organized by the Society for Experimental Mechanics, and held in
GardenGrove,California,January30–February2,2017.ThefullproceedingsalsoincludevolumesonNonlinearDynamics;
DynamicsofCivilStructures;ModelValidationandUncertaintyQuantification;DynamicsofCoupledStructures;Sensors
andInstrumentation;StructuralHealthMonitoring&DamageDetection;RotatingMachinery,HybridTestMethods,Vibro-
Acoustics and Laser Vibrometry; Shock & Vibration, Aircraft/Aerospace and Energy Harvesting, and Topics in Modal
Analysis&Testing.
Eachcollectionpresentsearlyfindingsfromexperimentalandcomputationalinvestigationsonanimportantareawithin
Structural Dynamics. Special Topics in Structural Dynamics represents papers on enabling technologies for General
DynamicsinbothModalAnalysisMeasurements,&SystemIdentification;andDamageDetection.
Theorganizerswouldliketothanktheauthors,presenters,sessionorganizers,andsessionchairsfortheirparticipationin
thistrack.
Sheffield,UK NikolaosDervilis
v
Contents
1 HarmonicForcingofaTwo-SegmentEuler-BernoulliBeam....................................................... 1
ArnaldoJ.MazzeiandRichardA.Scott
2 A New Surrogate Modeling Method Associating Generalized Polynomial Chaos Expansion
andKrigingforMechanicalSystemsSubjectedtoFriction-InducedVibration ................................. 17
E.Denimal,L.Nechak,J.-J.Sinou,andS.Nacivet
3 Multi-ObjectiveParametricOptimizationofanEquilibratorMechanism....................................... 25
ErginKurtulmus
4 DevelopmentofaNumericalModelforDynamicAnalysisofaBuilt-UpStructurebyaTwo-Step
FEM-TestCorrelationApproach...................................................................................... 41
VigneshJayakumarandJayKim
5 TestingMethodsforVerificationofaMountedAccelerometerFrequencyResponse ........................... 53
MarineDumont,DavidKuntz,andThomasPetzsche
6 ExperimentalEvaluationandStatisticalAnalysisofSynchronousAveraging ................................... 67
V.Camerini,G.Coppotelli,andS.Bendisch
7 OptimizationofaZigzagShapedEnergyHarvesterforWirelessSensingApplications........................ 85
BrittanyC.Essink,RobertB.Owen,andDanielJ.Inman
8 FuzzyFiniteElementModelUpdatingUsingMetaheuristicOptimizationAlgorithms......................... 91
I.Boulkaibet,T.Marwala,M.I.Friswell,H.H.Khodaparast,andS.Adhikari
9 TheCombinationofTestingand1DModelingforBoomingNoisePredictionintheModelBased
SystemTestingFramework............................................................................................. 103
FábioLuisMarquesdosSantos,TristanEnault,JanDeleener,TomVanHoucke,
andHermanVanderAuweraer
10 StructuralCouplingAnalysesofExperimentalModelsinaVirtualShakerTestingEnvironment
forNumericalPredictionofaSpacecraftVibrationTest ........................................................... 113
S.Waimer,S.Manzato,B.Peeters,M.Wagner,andP.Guillaume
11 EstablishmentofFull-Field,Full-OrderDynamicModelofCableVibrationbyVideoMotion
Manipulations............................................................................................................ 127
LorenzoSanchez,HuiyingZhang,AlexanderRoeder,JohnBowlan,JaredCrochet,YongchaoYang,
CharlesFarrar,andDavidMascareñas
12 AnalysesofTargetDefinitionProcessesforMIMORandomVibrationControlTests.......................... 135
UmbertoMusella,GiacomoD’Elia,SimoneManzato,BartPeeters,PatrickGuillaume,
andFrancescoMarulo
13 MaterialCharacterizationofSelf-Sensing3DPrintedParts....................................................... 149
DeryaZ.Tansel,JenniferA.Yasui,BenjaminJ.Katko,AlexandriaN.Marchi,andAdamJ.Wachtor
vii
viii Contents
14 TrajectoryTrackingandActiveVibrationSuppressiononaFlexibleTowerCrane ............................ 159
O.A.Garcia-Perez,G.Silva-Navarro,andJ.F.Peza-Solis
15 OnaGreyBoxModellingFrameworkforNonlinearSystemIdentification ..................................... 167
T.J.Rogers,G.R.Holmes,E.J.Cross,andK.Worden
16 In-ProcessMonitoringofAutomatedCarbonFibreTapeLayupUsingUltrasonicGuidedWaves............ 179
R.Fuentes,E.J.Cross,N.Ray,N.Dervilis,T.Guo,andK.Worden
17 DevelopmentofaMathematicalModeltoDesigntheControlStrategyofaFullScaleRoller-Rig............ 189
FerruccioResta,EdoardoSabbioni,DavideTarsitano,DinoDeva,DanieleTermini,andAlvaroFumi
Chapter 1
Harmonic Forcing of a Two-Segment Euler-Bernoulli Beam
ArnaldoJ.MazzeiandRichardA.Scott
Abstract Thisstudyisontheforcedmotionsofnon-homogeneouselasticbeams.Euler-Bernoullitheoryisemployedand
applied to a two-segment configuration subject to harmonic forcing. The objective is to determine the frequency response
functionforthesystem.Twodifferentsolutionstrategiesareused.Inthefirst,analyticsolutionsarederivedforthedifferential
equationsforeachsegment.Theconstantsinvolvedaredeterminedusingboundaryandinterfacecontinuityconditions.The
response,atagivenlocation,canbeobtainedasafunctionofforcingfrequency(FRF).Theprocedureisunwieldy.Moreover,
determiningparticularintegralscanbedifficultforarbitraryspatialvariations.Analternativemethodisdevelopedwherein
materialandgeometricdiscontinuitiesaremodeledbycontinuouslyvaryingfunctions(herelogisticfunctions).Thisresults
inasingledifferentialequationwithvariablecoefficients,whichissolvednumerically,forspecificparametervalues,using
MAPLE®. The numerical solutions are compared to the baseline analytical approach for constant spatial dependencies.
Forvalidationpurposesanassumed-modessolutionisalsodeveloped.Forafree-fixedboundaryconditionsexamplegood
agreementbetweenthenumericalmethodsandtheanalyticalapproachisfound,lendingassurancetothecontinuousvariation
model.Fixed-fixedboundaryconditionsarealsotreatedandagaingoodagreementisfound.
Keywords Beamswithlayeredcells • Layeredstructuresresonances
Nomenclature
A Areaofthebeamcrosssection(A,areaofi-cell)
i
B Constants
i
E Young’smodulus(E,Young’smodulusofi-cell)
i
F Externalforcing(spatialfunction,F,actingoni-cell)
i
f Externaltransverseforceperunitlengthactingonthebeam(f,actingoni-cell)
i
H(x) Logisticfunction
I Areamomentofinertiaofthebeamcrosssection(I,momentofinertiaofi-cell)
i
L Lengthofthebeam(L,lengthofi-cell)
i
R Spatialfunction,(forassumedsolution,R oni-cell)
i
t Time
w Beamtransversaldisplacement
xyz Inertialreferencesystem(coordinatesx,y,z)
Y Non-dimensionalbeamdisplacementinthey(transverse)direction
(cid:2) Non-dimensionalfrequency((cid:2)D(cid:3)2)
(cid:4) Massdensity((cid:4),densityofi-cell)
i
(cid:5) Non-dimensionalspatialcoordinate
(cid:6) Non-dimensionaltime
! Frequencyofharmonicexcitation
(cid:7) Referencefrequency
0
A.J.Mazzei((cid:2))
DepartmentofMechanicalEngineering,C.S.MottEngineeringandScienceCenter,KetteringUniversity,
1700UniversityAvenue,Flint,MI48504,USA
e-mail:[email protected]
R.A.Scott
UniversityofMichigan,HerbertH.DowBuilding,2300Hayward,AnnArbor,MI48109,USA
©TheSocietyforExperimentalMechanics,Inc.2017 1
N.Dervilis(ed.),SpecialTopicsinStructuralDynamics,Volume6,ConferenceProceedings
oftheSocietyforExperimentalMechanicsSeries,DOI10.1007/978-3-319-53841-9_1
2 A.J.MazzeiandR.A.Scott
1.1 Introduction
This work is an extension of one given in reference [1] in which the determination of the bending natural frequencies of
beams whose properties vary along the length was sought. Of interest were beams with different materials and varying
cross-sections,whichwerelayeredincellsandcouldbeuniformornot.
Inreference[1]anapproachwasdiscussed,inwhichthediscretecellpropertiesweremodeledbycontinuouslyvarying
functions,specificallylogisticfunctions,whichhadtheconsiderableadvantageofworkingwithasingledifferentialequation
(albeit one with variable coefficients). Natural frequencies could be calculated via a forced motion strategy by means of
MAPLE®’sODE1solver.
Thereareseveralreferencesonvibrationsoflayeredbeams.Forexamplereference[2],wherefreevibrationsofstepped
Timoshenko beams were treated via a Lagrange multiplier formalism. Results compared well with values obtained using
otheranalyticalmethods.Inreference[3]Euler-BernoullisteppedbeamswerestudiedviaexactandFEMapproaches.FEM
resultsusingnon-integerpolynomialsshapefunctions[4]comparedwellwithexactsolutions.Generalstudiesonmediawith
discretelayershavebeengiven,forexample,inreferences[5–8].Notethatfinitedifferenceapproachestothedynamicsof
non-homogeneousmediacanbefoundinreference[9].
Here the objective is to determine the frequency response functions (FRF) of such beams. Euler-Bernoulli theory is
used for a two-segment configuration under harmonic forcing. Analytic solutions can be obtained for each segment, for
specificconditions,andtheresponsecalculatedatagivenlocation,thusprovidingtheFRFs.Buttheprocedureisunwieldy
and particular solutions to the differential equations can be difficult to obtain for arbitrary spatial variations. The alternate
approachutilizedinvolvesmodelingmaterialandgeometricdiscontinuitiesbycontinuouslyvaryingfunctions.Thisresults
in a single differential equation with variable coefficients, which is solved numerically. These are compared to analytical
solutionsforconstantspatialdependencies.Anassumed-modessolutionisalsodevelopedforvalidationpurposes.
1.2 BasicProblem
InthisstudyEuler-Bernoullibeamtheoryisused.TheequationofmotionisgivenbelowandFig.1.1exhibitstheunderlying
variables.
(cid:2) (cid:3)
@2 @2w.x;t/ @2w.x;t/
E.x/I.x/ C(cid:4).x/A.x/ Df .x;t/ (1.1)
@x2 @x2 @t2
In the derivation of Eq. (1.1) no assumption was made in relation to the material type, therefore it can be either a
homogeneousoranon-homogeneousmaterial.
Fig.1.1 Beamelement
1www.maplesoft.com.
1 HarmonicForcingofaTwo-SegmentEuler-BernoulliBeam 3
The layered configuration discussed here is a two-cell beam. Strategies for obtaining the steady state response, due to
harmonicforcing,areinvestigatedinthefollowing.
1.3 AnalyticalApproach
Inthissectionanalyticsolutionsaresoughtusingstandardbeamtheory.
ConsiderthebeamshowninFig.1.2whichiscomposedbytwocellsofdifferentmaterials.
Thetransversaldisplacementequationofmotionforeachsegment(“i-th”segment)is:
(cid:2) (cid:3)
@2 @2w .x;t/ @2w .x;t/
E.x/I.x/ i C(cid:4).x/A.x/ i Df .x;t/;iD1;2::: (1.2)
@x2 i i @x2 i i @t2 i
wheref areexternaltransverseforcesperunitlength.
i
Forharmonicforcingwithfrequency!:
f .x;t/DF.x/sin.!t/ (1.3)
i i
Assumingsolutionsoftheform:
w .x;t/DR.x/sin.!t/ (1.4)
i i
leadsto
(cid:2) (cid:3)
d2 d2R.x/
EI i (cid:2)(cid:4)A!2R.x/DF.x/ (1.5)
dx2 i i dx2 i i i i
ForA,(cid:4),I andE constantineachsegment:
i i i i
d4R.x/ (cid:4)A F.x/
i (cid:2) i i!2R.x/D i (1.6)
dx4 EI i EI
i i i i
Define(cid:8)4 D (cid:4)iAi!2andP.x/D Fi.x/,thenforeachsegment:
i EiIi i EiIi
d4R.x/
i (cid:2)(cid:8)4R.x/DP.x/ (1.7)
dx4 i i i
Generalsolutionstothelineardifferentialequation(1.7)canbewrittenas:
R.x/DR .x/CR .x/ (1.8)
i ih ip
whereR (x)arethegeneralsolutionstothehomogeneousequationsandR (x)are“particularintegrals”.
ih ip
ForEq.(1.7),
R1h.x/DB1cosh.(cid:8)1x/CB2sinh.(cid:8)1x/CB3cos.(cid:8)1x/CB4sin.(cid:8)1x/ (1.9)
R2h.x/DB5cosh.(cid:8)2x/CB6sinh.(cid:8)2x/CB7cos.(cid:8)2x/CB8sin.(cid:8)2x/ (1.10)
Fig.1.2 Layeredbeam