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Vibration damping properties of porous materials
L. Rouleau1, A. Guinault2, J.-F. Deü1
1 Structural Mechanics and Coupled Systems Laboratory, Cnam Paris, France2 Arts et Métiers ParisTech - PIMM, Paris, France
Introduction Measurements Numerical simulations Conclusions and Perspectives
IntroductionIndustrial context
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 2/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
IntroductionMain NVH treatments in a vehicle
Sound absorbing materials (e.gporous materials)
Vibration damping materials(e.g. elastomers)
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 3/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
IntroductionMain NVH treatments in a vehicle
Sound absorbing materials (e.gporous materials)
Vibration damping materials(e.g. elastomers)
Vibration damping propertiesof porous materials ?
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 3/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
IntroductionContext of this work
Inter-laboratory tests on elastic characterization of poro- and visco-elasticmaterials for vibro-acoustic applications.
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 4/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
IntroductionIndustrial context
1 Introduction
2 MeasurementsExperimental set-upMaster curves through time-temperature superposition principle
3 Numerical simulations
4 Conclusions and Perspectives
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 5/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
MeasurementsExperimental set-up
Oscillatory rheometer in torsion MCR 502 (Anton Paar)
τ0γ0
t
φ/ω
|G∗|
Complex shear modulus1:G∗(ω,T ) = |G∗(ω,T )| exp(iφ(ω,T ))
1Etchessahar et al., Journal of the Acoustical Society of America, 117, 2005lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 6/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
MeasurementsExperimental set-up
Preparation of samplesCutting of cylindrical samples (24 mm diameter and 25 mm thickness)using gasket punches.
Use of a two sided bonded tape (for rough surface use) to glue the samplesto the parallel plates of the rheometer.
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 7/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
MeasurementsExperimental set-up
Test configurationFrequency range : [0.01Hz , 20Hz ]Temperature range : [−10oC , 20oC ]
Dynamic strain : 0.1% (linear viscoelasticity)
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 8/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Measurements of melamine foam’s complex shear modulusTime-temperature superposition principle
Measurements of G ′(f ,T ) and G ′′(f ,T )
TTSP↓
Shifting ofisotherms
10−1
100
101
102
103
104
105
103
104
105
Frequence [Hz]
Sto
rage
and
loss
mod
uli [
Pa]
Melamine foam
G’(ω) − Sample 1
G’’(ω) − Sample 1
G’(ω) − Sample 2
G’’(ω) − Sample 2
Master curves at Tref = 20oC
Principle of time-temperature principle 2:fred = aT(Ti )f
|G∗(fred,T0)| = bT(Ti )|G∗(f ,Ti )|φ(fred,T0) = φ(f ,Ti )
Computation of shift coefficients according to 3
2J. D. Ferry, Viscoelastic properties of polymers, 19803L. Rouleau et al, Mechanics of materials, 65, 2013
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 9/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Measurements of melamine foam’s complex shear modulusMaster curves at 20oC
10−1
100
101
102
103
104
105
103
104
105
Frequence [Hz]
Sto
rage
and
loss
mod
uli [
Pa]
Melamine foam
G’(ω) − Sample 1
G’’(ω) − Sample 1
G’(ω) − Sample 2
G’’(ω) − Sample 2
Light frequency dependence of melamine foam’s propertiesLight damping (ηmax = 0.12)
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 10/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Measurements of K-Flex ST’s complex shear modulusTime-temperature superposition principle
Measurements of G ′(f ,T ) and G ′′(f ,T )
TTSP↓
Shifting ofisotherms
10−2
100
102
104
106
103
104
105
106
Frequence [Hz]
Sto
rage
and
loss
mod
uli [
Pa]
K−Flex ST − Sample 1
G’(ω) − Sample 1
G’’(ω) − Sample 1
G’(ω) − Sample 2
G’’(ω) − Sample 2
Master curves at Tref = 20oC
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 11/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Measurements of K-Flex ST’s complex shear modulusMaster curves at 20oC
10−2
100
102
104
106
103
104
105
106
Frequence [Hz]
Sto
rage
and
loss
mod
uli [
Pa]
K−Flex ST − Sample 1
G’(ω) − Sample 1
G’’(ω) − Sample 1
G’(ω) − Sample 2
G’’(ω) − Sample 2
Strong frequency dependence of melamine foam’s propertiesModerate damping (ηmax = 0.48)
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 12/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Numerical simulationDescription of test cases
Simply supported plate
(Q20 elements - ≈ 71000 dofs)
Aluminium base panel : 420mm ×360mm ×3mmPorous layer : 420mm ×360mm ×25mm
Viscoelastic model to describe frequency-dependent properties
G∗(ω) =G0 + G∞(iωτ)α
1 + (iωτ)α
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 13/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Numerical simulationViscoelastic models
KFlex-ST
G0 = 1.31 104Pa G∞ = 2.11 106Pa τ = 4.70 10−8s α = 0.30lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 14/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Numerical simulationViscoelastic models
Melamine foam
G0 = 4.79 104Pa G∞ = 8.63 104Pa τ = 0.132s α = 0.43lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 15/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Numerical simulationFrequency responses
Frequency response of the panel to a point excitation
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 16/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Conclusions
Appropriate method to characterize the viscoelastic properties of porousmaterialsGood repeatability of measurementsStrong frequency-dependency of KFlex-ST properties as opposed themelamine foamFractional derivative models allow a good representation of thefrequency-dependency of porous materials’ propertiesBroadband vibration reduction due to the viscoelastic properties of someporous materials
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 17/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
PerspectivesExperimental vibration analysis of panels with porous materials
I Comparison of frequency responsesI Feasability of characterization through inverse
techniques
Carry out vibro-acoustic simulations to estimate the role of viscoelasticdamping of porous materials on the radiated/transmitted sound.
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 18/19
Introduction Measurements Numerical simulations Conclusions and Perspectives
Thank you for your attention.
http://www.lmssc.cnam.fr/en
lucie.rouleau@cnam.fr
lucie.rouleau@cnam.fr WMBR 2017 06/12/2017 19/19
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