experimental characterization of damped cfrp materials

Research ArticleExperimental Characterization of Damped CFRP Materials withan Application to a Lightweight Car Door

Alessandro Fasana Alessandro Ferraris Andrea Giancarlo AiraleDavide Berti Polato andMassimiliana Carello

Politecnico di Torino Turin Italy

Correspondence should be addressed to Alessandro Ferraris alessandroferrarispolitoit

Received 12 May 2017 Accepted 19 July 2017 Published 24 August 2017

Academic Editor Feng Zhu

Copyright copy 2017 Alessandro Fasana et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents a complete design procedure for defining a dynamic model of a Carbon Fibre Reinforced Polymer (CFRP)component with an embedded dampingmaterial layerThe experiment to determine themechanical characteristics of thematerialsis performed by the Oberst beam technique to provide precise material properties for a Finite Element (FE) model The techniqueimplemented namely the Linear Identification by Polynomial Expansion in the Z-domain (LIPEZ) method is used to comparethe experimental data with the numerical simulation results provided by the modal parameters to be compared with the numericalresults Two automotive components (a leaf spring and an outer shell of front door) have been testedThe research revealed the utterimportance of a correct definition of the geometry for the numerical models Finally the positive effects for acoustic performancewith a thin layer of KRAIBON SUT960924 damping material included in the stacking sequence of the CFRP component arehighlighted

1 Introduction

Recently car buyers have raised their expectation on vehiclecomfort with respect to the past when performances andreliability were sufficient to set the quality of the vehiclesVehicle electrification in this contest emphasizes the Noiseand Vibration Harshness (NVH) because of the absenceof the thermal engine noise and the more wide use oflightweight material [1ndash4] Carbon fibre reinforced plastic(CFRP) materials provide good mechanical characteristicsand promote light structures but emphasized NVH at thesame time For this reason the use of damping materialsin passive constrained layer configuration is often takeninto consideration [5] to lower the vibrational response ofCFRP structures but such procedure increases both theweight and the manufacturing process A precise numericalmodel for example a finite element model (FEM) of astructure is only reliable if material properties are correctlydefined so that Section 2 deals with the use of the so-calledOberst test method [6ndash8] to define Young modulus lossfactor of damping and structural materials These properties

have been calculated through the analysis of the frequencyresponse of tested samples measured at different tempera-tures in controlled climatic condition As expected the CFRPproperties do not change while the damping material and theresult show a quite typical viscoelastic behaviour

With the aim of defining a complete design procedure forCFRP (automotive) components with an embedded dampinglayer the comparison of the numerical (from a FEM) and themeasured mode shapes (from experimental modal analysis)is the most feasible and diffused procedure [9 10] Overthe last few decades a number of papers dealing withthe problem of modal parameters estimation of vibratingstructures have been presented [11ndash13] are good examplesThe linear identification by polynomial expansion in the Z-domain (LIPEZ) method adopted in this paper starts fromthe rational fraction polynomials (RFP) representation ofthe frequency response function (FRF) and expounds a totalleast square method in the Z-domain [14] The procedureis briefly presented in Section 3 In particular the methodis applied [15] to two automotive components which arealso reproduced at simulation level with computational FEM

HindawiShock and VibrationVolume 2017 Article ID 7129058 9 pageshttpsdoiorg10115520177129058

2 Shock and Vibration

Figure 1 The Oberst beam test bench

simulation in order to perform a correlation analysis Thechosen components include a leaf spring (Section 4) withsimple geometry and a door panel (Section 5) for its influencein vehicle global NVH characteristics Both components aremade with structural CFRP whose mechanical propertieshave been examined in Section 2 using the Oberst beam testmethod

2 CFRP and DampedSandwich Characterization

This section describes the procedure adopted to measureYoungrsquosmodulus and the loss factor of twodifferentmaterialsa set of pure T300 epoxy twill CFRP [0900] specimens anda set of 5 layers sandwich specimens with the following stak-ing sequence [090] CFRP + 1 Layer KRAIBON SUT960924+ [090] CFRP structure combining interlaminar dampingmaterial with 2 layers of CFRP T300 The activity aims atdefining the characteristics of the materials which is goingto be introduced in the material card of a FE simulation

The Oberst beam test is a standard method [6] to charac-terize laminatedmaterials and basically consist in a clamped-free beam as shown in Figure 1 The beam is excited by acontactless electromagnetic transducer which exerts a swept-sine force The input force frequency range depends on thetype of specimen under test Another contactless capacitivetransducer is located at the tip of the beam todetect the outputresponse (velocity) the spectrum of the output identifies thenatural frequencies of the beam and its loss factor In itssimplest form the identification procedure is based on theminus3 dB method (or half-power method) but more objectiveresults can be achieved by implementing a least squarefitting of the spectrum By analyzing the natural frequencieswith Bernoulli-Euler beam model Youngrsquos modulus can bedetermined

Tests have been performed in a thermally controlledenvironment at different temperatures from minus20∘C to +60∘Cwith steps of 10∘CThe first natural frequency has always beendiscarded since it can be too much affected by the imperfectconstraint conditions [2]Three samples of eachmaterial havebeen aged for (250 500 and 750 h) and then tested to estab-lish the effect of aging on damping capabilities of the inter-laminar material Table 1 gives the mean characteristics of thethree samples while Figure 2 presents the average variationof Youngrsquos modulus and loss factor with frequencyTheCRFPT300 (Figure 2) has very stable properties and very lowdamp-ing (lt1) while the sandwich configurationmdashCFRP T300+ KRAIBON SUT960924 (Figure 3)mdashshows the typical

T300 3L 0 h E modulusT300 3L 0 h loss factor

0

5

10

15

20

25

30

35

Youn

g m

odul

us (G

Pa)

minus10 0 10 20 30 40 50 60minus20Temperature (∘C)

0

005

01

015

02

025

03

Loss

fact

or [

]

Figure 2 Material characteristics as a function of temperatureCFRP T300 material


0

005

01

015

02

03

025

Loss

fact

or [

]

0

5

10

15

20

25

30

35

Youn

g m

odul

us (G

Pa)

Sandwich SUT 9609 0 h young modulusSandwich SUT 9609 0 h loss factor

Figure 3Material characteristics as a function of temperature T300+ KRAIBON SUT960924 sandwich

variations of viscoelastic materials and very good dampingin the whole temperature range 0ndash30∘C

The definition of the mechanical properties of thesematerials paves the way to their application to two testcases a CFRP leaf spring and a CFRP car door panel withor without a damping material in the constrained layerconfiguration The numerical results obtained by a FEMhave been compared to experimental results in terms ofnatural frequencies andmode shapes extracted by the LIPEZmethod

3 Outline of the LIPEZ Method

The LIPEZ method is a frequency domain modal param-eter extraction technique which takes advantage of the Z-transform formulation The procedure is briefly summarizedin this section but its complete description is found in [14]

For a linear and time invariant system with n degrees offreedom the FRF can be expressed by

119867119896 =2119899sum119903=1

119860119903 119911119896119911119896 minus 119911119903 (1)

Shock and Vibration 3

Table 1 Mean characteristics of the samples

Sample Layers Thickness (mm) Length (mm) Mass (kg) Density (kgm3)CFRP T300 3 091 25988 000393 1305KRAIBON SUT960924 3 + 1 + 3 172 25975 00074 1308

where 119867119896 = 119867(Ω119896) is the generic spectral line of the FRFevaluated at frequency

Ω119896 = (119896 minus 1) ΔΩ = (119896 minus 1) 2120587Δ119891 = 120587119891119904 (119896 minus 1)119873 minus 1 (2)

where 119891119904 is the sampling frequency Δ119891 is the frequencyresolution 119873 is the number of spectral lines and 119896 = 1 119873

The terms related to the 119885-transform are119911119903 = 119890119904119903Δ119905119911119896 = 119890119894(119896minus1)ΔΩΔ119905 = 119890119894120587(119896minus1)(119873minus1)

(3)

where 119894 = radicminus1 and the poles 119904119903 are linked to the natural angu-lar frequencies 120596119903 and damping ratios 120585119903 by the expression119904119903 = minus120585119903120596119903 + 119894120596119903radic1 minus 1205852119903

The sum in (1) can be converted in the following rationalfraction expression

119867119896 = 1198871119911119896 + sdot sdot sdot + 119887211989911991121198991198961198860 + 1198861119911119896 + sdot sdot sdot + 1198862119899minus11199112119899minus1119896 + 1199112119899

119896

(4)

where the 4119899 unknown coefficients 1198860 1198862119899minus1 and 1198871 1198872119899 are real valued Equation (4) can be written for119873 spectrallines and for many FRFs (namely NFRF) to get an overdeter-mined linear system of equations

[[[[[

A1

ANFRF

]]]]]a + [[[[[

minusB sdot sdot sdot 0 d

0 sdot sdot sdot minusB

]]]]]

b1

bNFRF

=

w1

wNFRF

(5)

where a = [1198860 1198861 sdot sdot sdot 1198862119899minus1]T and bm =[1198871 1198872 sdot sdot sdot 1198872119899]Tm (119898 = 1 NFRF) are the vectors tobe determined The matrix in (5) can surely be solved butthe procedure can be time-consuming especially when largedata sets are analyzed (NFRF ≫ 1) and n has to vary (egto define a stabilization chart) A much quicker least squareprocedure can indeed be implemented to limit at first thesolution to vector a

Ra = r (6)

The real square (2119899 times 2119899) and well-conditioned matrix Rcontains the information of all the measured FRFs but asystem of only 2119899 equations has to be solved The poles 119904119903 =ln 119911119903Δ119905 can then be obtained by using the equation

1198860 + 1198861119911 + sdot sdot sdot + 1198862119899minus11199112119899minus1 + 1199112119899 = 0 (7)

Any vector b119898 the related modal constants 119860119903 and eventu-ally the mode shapes can then be recovered from (4)

An open source version of the implemented method canbe obtained from the authors under the CC BY license

Figure 4 The leaf spring component the experimental configura-tion with 23 accelerometers

Figure 5The leaf spring component the finite element model witha detailed view

4 Leaf Spring Application

This section is devoted to the comparison of the numer-ical simulation and experimental results of a CRFP leafspring formed by 31 layers of Epoxy CFRP T300 twill 2 times2 240 grm2 following the stacking sequence [0(045)1400]

41 Experimental Tests The test aims at computing themodalparameters of the system in the free-free condition with thecomponent vertically suspended by elastic supports as shownin Figure 4 or by a Single Point Constrain (green in Figure 5)The leaf spring was excited by an electromagnetic shaker


200 300 400 500 600 700 800 900 1000100Frequency (Hz)

0

5

10

15

20

25M

odel

ord

er s

um (a

bs(F

RFs)

)

Figure 6 Stabilization diagram for the natural frequencies Each ldquo+rdquocorresponds to an estimated frequency in the selected band giventhe model order 119899 (ranging from 1 to 25)

driven by a white noise input signal in the frequency range2ndash1000Hz A 24-channel signal acquisition board (OROSOR38) was used to simultaneously record the responsesof 23 piezoelectric accelerometers (outputs) and the forceactuation force is delivered to the beam by a load cell posi-tioned in the right bottom corner Considering the leaf springdimensions one set of properly distributed accelerometersis sufficient to investigate the vibrational behaviour of thecomponent

Time domain input (force) and output (acceleration)data have been processed according to the Hv estimator[16] to produce the FRFs which are the required inputs forthe LIPEZ method The coherence functions (not reportedhere for the sake of brevity) confirm the validity of theexperimental setup showing local minima much lower thanone only at resonances and antiresonances Also the inputspectrum is reasonably flat except near resonances All datacan be obtained from the authors

The unknown model order n that is the number ofmodes is increased from a minimum to a maximum value(1ndash25) and the results are plotted in stabilization chartsFigures 6 and 7 present the stabilization diagrams of naturalfrequencies and damping ratios overlaid on the sum of themoduli of all FRFs Separating physical from computationalmodes is very simple as very stable frequency lines can beobserved in Figure 6 A slight scatter of damping ratios isobserved in Figure 7 but the modal damping is always verylow (lt05)

42 Finite Element Model The simple geometry of the itemand the detailed characterization of the material proper-tiesmdashdescribed in Section 2mdashallowed defining an accurateFE model by using Altair Hypermesh (Optistruct implicitsolver) as specified in [17 18] The FE model precisely takesinto account the stacking sequence and orientation of theplies of the actual leaf spring whose production process wasstrictly controlled in all its steps from the selection of the

400 600 800 1000200Frequency (Hz)

0

02

04

06

08

Dam

ping

()

Figure 7 Stabilization diagram for the damping ratios Each ldquolowastrdquocorresponds to a pair natural frequency-damping ratio given themodel order 119899 (ranging from 1 to 25) For somemodes for examplemode 2 at about 200Hz many points are almost completelysuperimposed

materials to the final curing of the componentThe 31 plies ofCFRP have been modelled as a composite laminate by usingthe ldquoPCOMPPrdquo property card and the material card ldquoMAT8rdquo The property is chosen because it gives the possibilityof characterizing layer by layer the laminate defining thestacking sequence thickness material and orientation ofeach layer The material card has been chosen because itis the only one dedicated for PCOMPP property whichpermits the implementation of orthotropic characteristics forshell elements as defined in [17 18] Material characteristicsimplemented in the virtual model are defined as follows

(i) Young modulus 1198641 = 1198642 = 44700MPa(ii) 11986612 = 2500MPa(iii) Poisson ratio 12059212 = 003(iv) Density 120588 = 1460 kgm3(v) Loss factor 120578 = 0004

The component is meshed with about 7000 shell elementswith mean shell size of 5mm which well subdivide theentire surface of the component The elements dimensionhas been properly defined by means of convergence test notreported for the sake of brevity [19] Shell elements have beenchosen because of model complexity reduction consideringthat stresses distribution along the thickness can be neglectedNo constraints are applied to themodel to simulate a free-freecondition replicating the real test

It is important to point out that the first six vibratingmodes (at almost zero frequency) describe the rigid bodymotion and are not be taken into account in the followinganalysis

The Lanczos algorithm [20 21] has been used to solvethe undamped eigenvalue problem the damping matrixis disregarded not only for limiting the numerical issuesbut also because as proven by the Oberst beam test and


Table 2 Natural frequencies damping ratios and MAC values for the leaf spring

Mode number 119891119873 (Hz) 119891119864 (Hz) Δ119891 () 120577119864 () Diag (MAC)1 6780 713 minus49 034 0982 1884 1947 minus32 021 0973 2383 2414 minus13 032 0974 3708 3754 minus12 020 0965 4524 4420 26 034 0966 6146 6144 00 021 0957 7488 7202 40 038 0938 8283 8516 minus27 029 0849 9198 8974 25 030 09110 10539 9945 60 049 087

the experimental modal analysis the damping capabilityof the CFRP is in fact very limited The damping matrixshould anyway be simply described by the proportionaldamping model because in this configuration damping canbe attributed to the inherent properties of the material

43 Comparison To evaluate the correlation between thenumerical analysis and the experimental results the ModalAssurance Criterion (MAC) is adopted as described in [5 6]

MAC119879119878 =100381610038161003816100381610038161003816120595119873119879 120595119864lowast

1003816100381610038161003816100381610038162

(120595119873119879 120595119873lowast) (120595119864119879 120595119864lowast) (8)

where 120595119873 and 120595119864 indicate numerical and experimentalmode shapes respectively This index indicates the similaritybetween the modes shapes and is equal to one when twocompared modes have exactly the same shape Figure 8 givesa pictorial representation of the MAC matrix while Table 2presents the numerical values on the main diagonal It canbe noticed that the minimum value is a very good (084 forthe first 10 analyzed modes) The same table also lists theexperimental and numerical natural frequencies showing aquite good correlation As expected modal damping ratiosare very limited

This first experiment validates the five steps of the designprocedure

(1) Characterize the materials(2) Carefully control the production of the component

especially the orientation of the fibres(3) Build a FEM which precisely reproduces the actual

geometry and stacking sequence(4) Experimentally extract the modal parameters(5) Compare the model with the experimental results

All of these steps are necessary to fulfil the request of a reliablemodel as clearly pointed out by the example described in thefollowing chapter

5 Car Door Case

The same design procedure has been followed on a moresophisticated test case a CRFP car door panel

12

34

56

78

910

12345678910

0

05

1M

AC in

dex

[]

Experimental modes N ∘ Simulated modes N∘

0

01

02

03

04

05

06

07

08

09

1

Figure 8 MAC coefficient for the leaf spring test

In modern light weight design for vehicles doors areformed by two separately produced thin shells of CFRPmaterial which are then tightly bonded along their outerborders The final structure is extremely lightweight butbecause of its relatively large and flat flexible surface theinfluence on the acoustic characteristics of the vehicle issignificant In order to decrease the sound emission of thestructure a thin layer of damping material has been insertedalong the stacking sequence mainly for two reasons firstof all it has to be stressed that the thin damping materialis positioned on the same mould as the other carbon fibrelayers and undergoes the same curing process as the standardCFRP material A single (proper) production sequence hasto be performed for both the CF and the damping layers sothat after curing the two separated panels there is no need tohandle again the two shells and the total cost can be reducedThe second reason is that the increment of the dampingproperties of the assembly is more controllable because theconstrained layer solution (CFRP-damper-CFRP) performsmuch better than the free layer solution (CFRP-damper)

In this section the comparison of numerical and exper-imental results of the external shell of a door panels are


Figure 9The door panel experimental configurationwith 23 accel-erometers a load cell (red arrow) and 44 measurement points

20 30 40 5010Frequency (Hz)

0

1

2

3

4

5

6

Dam

ping

()

Figure 10 The door panel stabilization diagram for the dampingratios each ldquolowastrdquo corresponds to a pair natural frequency-dampingratio

presented with or without the integrated damping materiallayer

51 Experimental Tests The external shell of the door wastested in free-free conditions with a white noise excitationforce given through an electromagnetic shaker Again 23accelerometers and a load cell were used to record theresponse but in this case two repetitions were needed tomeasure 44 points aiming at a good mode shapes definition(Figure 9) The load cell was fixed on the left bottom cornerand a white noise excitation was generated in the 0ndash400Hzband The procedure followed for data acquisition is thesame as for the leaf spring and again coherence remainsalmost equal to one in all the analyzed frequency range thusconfirming the quality of the measured data

Some spurious (numerical) modes are extracted by theLIPEZmethod and theywere simply detected by checking thestabilization diagram of damping ratios (Figure 10) numer-ical and nonacceptable solutions correspond to unstable or

unrealistically high damping ratios that is the values in the8ndash16Hz band in Figure 10

The modal parameters extraction has been limited to thefrequency range 4ndash130Hz which contains 11 modes

52 Finite Element Model The shell of the door panel isa handmade component of CFRP layers but its productionmodel has been quality controlled to ensure an actualorientation of the fibres as accurate as possible Also thethickness of the shell has been carefully measured to limitthe undesired uncertainty which could occur in proximity ofsmall curvature radii

The FE models are defined to reproduce the real com-ponents with the same materials described in Section 2 Asummary of the FEMmain characteristics is as follows

(i) CFRP T300 material(ii) Orthotropic CFRP laminate [090]3(iii) Free-free condition (no model constraints)(iv) Element type shell(v) Maximum mesh size 4mm(vi) Eigenproblem solver Lanczos algorithm

53 Comparison The visual comparison confirmed by thevalues of the MACmatrix and the natural frequencies showsa really poor agreement between numerical and experimentalmode shapes For example Figure 11 gives a graphical repre-sentation of the MAC matrix which is disappointing

Since thematerial has been characterized according to theprocedure described in Section 2 (which leads to an excellentmodel for the leaf spring) and the experimental results arevery stable and reliable the issue may be related to the aspectthat does not match the requirements of the design sequencelisted in Section 43

The ideal disposition of the CF layers has accurately beenrespected at the production stage and later reproduced bythe FE model but the geometry was obtained by a sortof ldquoreverse engineeringrdquo process Unfortunately a completemathematical model of the mould is not available so that itssurface has been scanned by a laser The measured pointsform a basis for the ensuing CAD representation which inturn is the basis for the FE model It is then reasonable toattribute the differences between numerical and experimentalresults to an inaccurate geometry of the FEmodel A detailedrevision of the numerical model has then been carriedout with particular attention to a correct definition of thecurvature of the panelsThemacroscopic difference is almostnegligible for example themass variation is limited to amere014 but the refinement is essential to tune the dynamicproperties of the model and cope with the experimentalresults The MAC matrix represented in Figure 12 is still notas good as expected but at least for the first four modesthe coefficients (main diagonal) are above 90 confirmingthe impression given by the visual inspection of the modeshapes (Figure 13) Differences are still present and canbe attributed to both experimental and numerical issuesthe numerically redesigned geometry is not perfect yet the


12

34

56

12

34

56

0

05

1

MAC

inde

x [

]

0

01

02

03

04

05

06

07

08

09

1


Figure 11MAC coefficient for the door test before geometry refine-ment

12

34

56

78

910

12345678910 0

01

02

03

04

05

06

07

08

09

1

Experimental m

odes∘

Simulated modes ∘

0

05

1

MAC

inde

x [

]

23

45

67

8910

123456789

imental m

odes∘

ted modes ∘

Figure 12 MAC coefficient for the door test after geometry refine-ment

orientation of the carbon fibres is not completely identicalto the real components (the CFRP door panel is made bywarping the fabric on the mould orientation is complicatedfor surface with corners) the directions assigned to themeasured acceleration (which are used to define the 3Dmodeshapes on the basis of the identified eigenvectors 120595119864) haveinaccurately been measured and the mass of accelerometersload cell and cables is not negligible with respect to thestructure and alsomoves the system away from the ideal free-free conditions

The conclusion is that the exact definition of the geometryand the disposition of the fibres is compulsory for a correctsimulation of the dynamic behaviour of such extended andlightweight structures The simple check on the weight ofthe component and its qualitative visual examination are notsufficient to accept the model even if it is apparently verysimple

Table 3 Overall value of the FRFs for door panels

0ndash100 (Hz) 0ndash200 (Hz) 0ndash400 (Hz)Original (dB) 1061 1178 1234Damped (dB) 1030 1108 1151

54 Damped versus Undamped Configuration This sectioncompares the FRFs of the external shell of the door with andwithout an embedded layer of dampingmaterialThe originalshell is formed by six CF layers with total mass equal to209 kg which are almost unable to dissipate vibration energyas pointed out by the low valuesmodal damping ratios (about1 see Figure 10) A similar shell has been manufactured(same material and same orientation of the fibres) with a 3-1-3 stacking sequence the inner core is made of a KRAIBONSUT960924 damping layer which undergoes the same cur-ing cycle as the CFRP The SUT960924 damping material isdivided into two patches as sketched in Figure 14 and the totalmass of the damped door is 224 kg a very limited incrementwith respect to the undamped configuration

The two shells underwent the same experimental tests and44 FRFs were measured (see Figure 9) by using a randominput in the band 0ndash400Hz The effect of the dampingmaterial is obvious when listening to the sound emitted bythe two panels (undamped and damped) A quantificationof the effectiveness of the constrained layer is given inFigure 15 where the sum of the moduli of all 44 FRFs(inertance) is plotted the red dotted line (no damping) is wellabove the solid blue curve along the entire testing frequencyrange especially for frequency higher than 50Hz (which isimportant for limiting the interior noise harshness)

Table 3 gives the overall value of the FRFs that is thesum of the modals extended over a certain frequency rangefor the two configurations Even in the 0ndash100Hz region thedifference is above 3 dBs that is half-power and furtherlyincreases with the frequency band

6 Conclusions

Structural material properties have been determined by theOberst beam technique a database which permits reliablereproduction of experimental tests by a FE model has beendefined Both pure CFRP structures and sandwich structuresformed by CRFP and a damping material have been tested inthe temperature range minus20+60∘C to evaluate the variabilityof Youngrsquos modulus and the loss factor A couple of CFRPautomotive components a leaf spring and the external panelof a door have been manufactured and tested The compari-son of the experimental modal analysis with the results of theFE models revealed the two extreme important aspects Notonly has thematerial to be correctly defined but also a precisegeometry of the FEmodel should be created to achieve a goodcorrelation even small geometrical variations especially incurved and large surfaces can lead to significant differencesfor dynamic responses The influence of damping materialhas experimentally been verified and quantified on the doorpanel A thin layer of KRAIBON SUT960924 dampingmaterial has been embedded in the stacking sequence of


(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000

minus300minus200minus1000100 X

Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z

Undeformed shapeDeformed shape

(b)

Figure 13 The first two mode shapes after the geometry refinement (a) FEM (b) experimental

Figure 14 Comparison of the damped and undamped panelsposition of the damping patches

50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)

Figure 15 Comparison of the damped and undamped panelssum of the FRFs red dashed line undamped panel-blue solid linedamped panel


the panel with very limited impact on both the productionprocess and the final cost of the component The weighvariation of the panel is within +7 but its dynamic responsedramatically improved with potentially significant effects onthe noise harshness of the car interior environment

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge Altair-Italy Engineer-ing SRL for providing the FE software and GummiwerkKRAIBURG GmbH for the damping material ldquoKRAIBONSUT960924rdquo and the active support during all the activityand GAngeloni SRL for the structural CFRP material

References

[1] M Carello and A G Airale ldquoComposite Suspension ArmOptimization for the City Vehicle XAM 20rdquo in Design andComputation of Modern Engineering Materials A Ochsnerand H Altenbach Eds vol 54 pp 257ndash272 Cham SpringerInternational Publishing 2014

[2] M Carello A Airale A Ferraris and A Messana ldquoXAM20 from Student Competition to Professional ChallengerdquoComputer-Aided Design and Applications vol 11 pp S61ndashS672014

[3] M Carello A G Airale and A Ferraris ldquoCity vehicle XAM20design and optimization of the composite suspension systemrdquoSAE Technical Papers vol 1 pp 1ndash10 2014

[4] G Brusaglino G Buja M Carello A P Carlucci C H Onderand M Razzetti ldquoNew technologies demonstrated at FormulaElectric and Hybrid Italy 2008rdquo World Electric Vehicle Journalvol 3 no 1 pp 1ndash12 2009

[5] H Wan Y Li and L Zheng ldquoVibration and damping analysisof a multilayered composite plate with a viscoelastic midlayerrdquoShock and Vibration vol 2016 Article ID 6354915 10 pages2016

[6] Standard Standard Test Method for Measuring Vibration-Damping Properties of Materials ASTM International 2010

[7] G Erdogan F Bayraktar and K Y Sanliturk ldquoMeasurementof Dynamic Properties of Materialsrdquo in Proceedings of the32nd International Congress and Exposition on Noise ControlEngineering Jeju International Convention Center SeogwipoKorea August 2003

[8] J1637 Laboratory Measurement of the Composite VibrationDamping Properties of Materials on a Supporting Steel Bar -SAE International httpstandardssaeorgj1637 201306

[9] N M M Maia and J M Montalvao e Eds Theoretical AndExperimental Modal Analysis Research Studies Press NewYork NY USA 1997

[10] D J Ewins Modal Testing Theory Practice and ApplicationResearch Studies Press Philadelphia PA USA 2nd edition2000

[11] E Gandino L Garibaldi and S Marchesiello ldquoCovariance-driven subspace identification a complete input-output

approachrdquo Journal of Sound and Vibration vol 332 no 26 pp7000ndash7017 2013

[12] B Peeters H Van Der Auweraer P Guillaume and J LeuridanldquoThe PolyMAX frequency-domain method a new standard formodal parameter estimationrdquo Shock and Vibration vol 11 no3-4 pp 395ndash409 2004

[13] J Wang C Wang T Zhang and B Zhong ldquoComparisonof different independent component analysis algorithms foroutput-only modal analysisrdquo Shock and Vibration vol 2016Article ID 6309084 pp 1ndash25 2016

[14] A Fasana ldquoModal parameters estimation in the Z-domainrdquoMechanical Systems and Signal Processing vol 23 no 1 pp 217ndash225 2009

[15] A Fasana M Carello A Ferraris A Airale and D B PolatoldquoNVH Analysis of Automotive Components A Carbon FiberSuspension System Caserdquo in Advances in Italian MechanismScience G Boschetti and A Gasparetto Eds vol 47 pp 345ndash354 Springer International Publishing 2017

[16] K Shin and J K Hammond Fundamentals of signal processingfor sound and vibration engineers John Wiley and Sons Hobo-ken NJ USA 2008

[17] Altair Engineering Altair Engineering Practical Aspect of FiniteElement Simulation 3rd edition 2015

[18] Altair Engineering Altair engineering Pre and post ndash processingfor Finite Element Analysis guidebook 2015

[19] J Jin and D J Riley ldquoEffect of mesh size on finite elementanalysis of plate structurerdquo International Journal of EngineeringScience and Innovative Technology pp 181ndash185 2015

[20] J Rydh Very Large Symmetric Eigenvalue Problems Solvedby Lanczos and Multiple Relatively Robust Representations forTridiagonals School of Engineering Physics Royal Institute ofTechnology 2007

[21] Combining automated multilevel substructuring and subspaceiteration for huge gyroscopic eigenproblems ResearchGatehttpswwwresearchgatenetpublication259193426 Combin-ing automated multilevel substructuring and subspace itera-tion for huge gyroscopic eigenproblems

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Figure 1 The Oberst beam test bench

simulation in order to perform a correlation analysis Thechosen components include a leaf spring (Section 4) withsimple geometry and a door panel (Section 5) for its influencein vehicle global NVH characteristics Both components aremade with structural CFRP whose mechanical propertieshave been examined in Section 2 using the Oberst beam testmethod

2 CFRP and DampedSandwich Characterization

This section describes the procedure adopted to measureYoungrsquosmodulus and the loss factor of twodifferentmaterialsa set of pure T300 epoxy twill CFRP [0900] specimens anda set of 5 layers sandwich specimens with the following stak-ing sequence [090] CFRP + 1 Layer KRAIBON SUT960924+ [090] CFRP structure combining interlaminar dampingmaterial with 2 layers of CFRP T300 The activity aims atdefining the characteristics of the materials which is goingto be introduced in the material card of a FE simulation

The Oberst beam test is a standard method [6] to charac-terize laminatedmaterials and basically consist in a clamped-free beam as shown in Figure 1 The beam is excited by acontactless electromagnetic transducer which exerts a swept-sine force The input force frequency range depends on thetype of specimen under test Another contactless capacitivetransducer is located at the tip of the beam todetect the outputresponse (velocity) the spectrum of the output identifies thenatural frequencies of the beam and its loss factor In itssimplest form the identification procedure is based on theminus3 dB method (or half-power method) but more objectiveresults can be achieved by implementing a least squarefitting of the spectrum By analyzing the natural frequencieswith Bernoulli-Euler beam model Youngrsquos modulus can bedetermined

Tests have been performed in a thermally controlledenvironment at different temperatures from minus20∘C to +60∘Cwith steps of 10∘CThe first natural frequency has always beendiscarded since it can be too much affected by the imperfectconstraint conditions [2]Three samples of eachmaterial havebeen aged for (250 500 and 750 h) and then tested to estab-lish the effect of aging on damping capabilities of the inter-laminar material Table 1 gives the mean characteristics of thethree samples while Figure 2 presents the average variationof Youngrsquos modulus and loss factor with frequencyTheCRFPT300 (Figure 2) has very stable properties and very lowdamp-ing (lt1) while the sandwich configurationmdashCFRP T300+ KRAIBON SUT960924 (Figure 3)mdashshows the typical

T300 3L 0 h E modulusT300 3L 0 h loss factor

0

5

10

15

20

25

30

35

Youn

g m

odul

us (G

Pa)


0

005

01

015

02

025

03

Loss

fact

or [

]

Figure 2 Material characteristics as a function of temperatureCFRP T300 material


0

005

01

015

02

03

025

Loss

fact

or [

]

0

5

10

15

20

25

30

35

Youn

g m

odul

us (G

Pa)

Sandwich SUT 9609 0 h young modulusSandwich SUT 9609 0 h loss factor

Figure 3Material characteristics as a function of temperature T300+ KRAIBON SUT960924 sandwich

variations of viscoelastic materials and very good dampingin the whole temperature range 0ndash30∘C

The definition of the mechanical properties of thesematerials paves the way to their application to two testcases a CFRP leaf spring and a CFRP car door panel withor without a damping material in the constrained layerconfiguration The numerical results obtained by a FEMhave been compared to experimental results in terms ofnatural frequencies andmode shapes extracted by the LIPEZmethod

3 Outline of the LIPEZ Method

The LIPEZ method is a frequency domain modal param-eter extraction technique which takes advantage of the Z-transform formulation The procedure is briefly summarizedin this section but its complete description is found in [14]

For a linear and time invariant system with n degrees offreedom the FRF can be expressed by

119867119896 =2119899sum119903=1

119860119903 119911119896119911119896 minus 119911119903 (1)








(3)




119896

(4)


[[[[[

A1

ANFRF

]]]]]a + [[[[[



]]]]]

b1

bNFRF

=

w1

wNFRF

(5)


Ra = r (6)











200 300 400 500 600 700 800 900 1000100Frequency (Hz)

0

5

10

15

20

25M

odel

ord

er s

um (a

bs(F

RFs)

)






400 600 800 1000200Frequency (Hz)

0

02

04

06

08

Dam

ping

()












MAC119879119878 =100381610038161003816100381610038161003816120595119873119879 120595119864lowast

1003816100381610038161003816100381610038162

(120595119873119879 120595119873lowast) (120595119864119879 120595119864lowast) (8)







5 Car Door Case


12

34

56

78

910

12345678910

0

05

1M

AC in

dex

[]


0

01

02

03

04

05

06

07

08

09

1







0

1

2

3

4

5

6

Dam

ping

()














12

34

56

12

34

56

0

05

1

MAC

inde

x [

]

0

01

02

03

04

05

06

07

08

09

1



12

34

56

78

910

12345678910 0

01

02

03

04

05

06

07

08

09

1

Experimental m

odes∘

Simulated modes ∘

0

05

1

MAC

inde

x [

]

23

45

67

8910

123456789

imental m

odes∘

ted modes ∘









6 Conclusions



(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000


Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z


(b)



50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















(3)




119896

(4)


[[[[[

A1

ANFRF

]]]]]a + [[[[[



]]]]]

b1

bNFRF

=

w1

wNFRF

(5)


Ra = r (6)











200 300 400 500 600 700 800 900 1000100Frequency (Hz)

0

5

10

15

20

25M

odel

ord

er s

um (a

bs(F

RFs)

)






400 600 800 1000200Frequency (Hz)

0

02

04

06

08

Dam

ping

()












MAC119879119878 =100381610038161003816100381610038161003816120595119873119879 120595119864lowast

1003816100381610038161003816100381610038162

(120595119873119879 120595119873lowast) (120595119864119879 120595119864lowast) (8)







5 Car Door Case


12

34

56

78

910

12345678910

0

05

1M

AC in

dex

[]


0

01

02

03

04

05

06

07

08

09

1







0

1

2

3

4

5

6

Dam

ping

()














12

34

56

12

34

56

0

05

1

MAC

inde

x [

]

0

01

02

03

04

05

06

07

08

09

1



12

34

56

78

910

12345678910 0

01

02

03

04

05

06

07

08

09

1

Experimental m

odes∘

Simulated modes ∘

0

05

1

MAC

inde

x [

]

23

45

67

8910

123456789

imental m

odes∘

ted modes ∘









6 Conclusions



(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000


Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z


(b)



50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










200 300 400 500 600 700 800 900 1000100Frequency (Hz)

0

5

10

15

20

25M

odel

ord

er s

um (a

bs(F

RFs)

)






400 600 800 1000200Frequency (Hz)

0

02

04

06

08

Dam

ping

()












MAC119879119878 =100381610038161003816100381610038161003816120595119873119879 120595119864lowast

1003816100381610038161003816100381610038162

(120595119873119879 120595119873lowast) (120595119864119879 120595119864lowast) (8)







5 Car Door Case


12

34

56

78

910

12345678910

0

05

1M

AC in

dex

[]


0

01

02

03

04

05

06

07

08

09

1







0

1

2

3

4

5

6

Dam

ping

()














12

34

56

12

34

56

0

05

1

MAC

inde

x [

]

0

01

02

03

04

05

06

07

08

09

1



12

34

56

78

910

12345678910 0

01

02

03

04

05

06

07

08

09

1

Experimental m

odes∘

Simulated modes ∘

0

05

1

MAC

inde

x [

]

23

45

67

8910

123456789

imental m

odes∘

ted modes ∘









6 Conclusions



(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000


Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z


(b)



50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














MAC119879119878 =100381610038161003816100381610038161003816120595119873119879 120595119864lowast

1003816100381610038161003816100381610038162

(120595119873119879 120595119873lowast) (120595119864119879 120595119864lowast) (8)







5 Car Door Case


12

34

56

78

910

12345678910

0

05

1M

AC in

dex

[]


0

01

02

03

04

05

06

07

08

09

1







0

1

2

3

4

5

6

Dam

ping

()














12

34

56

12

34

56

0

05

1

MAC

inde

x [

]

0

01

02

03

04

05

06

07

08

09

1



12

34

56

78

910

12345678910 0

01

02

03

04

05

06

07

08

09

1

Experimental m

odes∘

Simulated modes ∘

0

05

1

MAC

inde

x [

]

23

45

67

8910

123456789

imental m

odes∘

ted modes ∘









6 Conclusions



(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000


Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z


(b)



50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

1

2

3

4

5

6

Dam

ping

()














12

34

56

12

34

56

0

05

1

MAC

inde

x [

]

0

01

02

03

04

05

06

07

08

09

1



12

34

56

78

910

12345678910 0

01

02

03

04

05

06

07

08

09

1

Experimental m

odes∘

Simulated modes ∘

0

05

1

MAC

inde

x [

]

23

45

67

8910

123456789

imental m

odes∘

ted modes ∘









6 Conclusions



(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000


Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z


(b)



50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










12

34

56

12

34

56

0

05

1

MAC

inde

x [

]

0

01

02

03

04

05

06

07

08

09

1



12

34

56

78

910

12345678910 0

01

02

03

04

05

06

07

08

09

1

Experimental m

odes∘

Simulated modes ∘

0

05

1

MAC

inde

x [

]

23

45

67

8910

123456789

imental m

odes∘

ted modes ∘









6 Conclusions



(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000


Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z


(b)



50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

minus2000

200400

600800

minus150minus100

minus50X

Y

minus2000

200400

600800

1000


Y

300

400

500

600

700

Z

100

200

300

400

500

600

700

800

Z


(b)



50 100 150 200 250 300 350 4000Frequency (Hz)

20

30

40

50

60

70

80

Sum

of t

he|２Ｍ |

(dB

- Ref

1m

Ｍ2

N)






Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









experimental characterization of damped cfrp materials

Documents