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