vibro-acoustic modelling of anisotropic poroelastic materials – characterisation of the...

Vibro-acoustic Modelling of AnisotropicPoroelastic Materials –

Characterisation of the Anisotropic Properties

Christophe Van der Kelen

Ph.D. defenseJanuary 20, 2014, Stockholm, Sweden

Vibro-acoustic Modelling of Anisotropic Poroelastic Materials– Characterisation of the Anisotropic Properties

Research areamodelling of the vibro-acoustic behaviour of poroelasticmaterials

Research objectivecharacterisation of the properties

Challengeanisotropy of the properties

Contributionscharacterisation methodology

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Vibro-acoustic Modelling of Anisotropic Poroelastic Materials– Characterisation of the Anisotropic Properties

Paper AC. Van der Kelen and P. Göransson,Identification of the full anisotropic flow resistivity tensor for multiple glass wool andmelamine foam samples.

Paper BC. Van der Kelen, P. Göransson, B. Pluymers, W. Desmet,On the influence of frequency-dependent elastic properties in vibro-acousticmodelling of poroelastic materials under structural excitation.

Paper CJ. Cuenca, C. Van der Kelen and P. Göransson,A general methodology for inverse estimation of the elastic and anelastic propertiesof anisotropic open-cell poroelastic materials - with application to a melamine foam,.

Paper DC. Van der Kelen, J. Cuenca and P. Göransson,A method for characterisation of the static elastic properties of the porous frame oforthotropic open-cell foams.

Paper EC. Van der Kelen, J. Cuenca and P. Göransson,A method for inverse estimation of the static elastic properties of anisotropicporoelastic foams - with application to a melamine foam.

3 / 28

Why poroelasticmaterials?

Why anisotropy?

Which properties?

How?

Summary

OutlineVibro-acoustic Modelling of Anisotropic Poroelastic Materials

– Characterisation of the Anisotropic Properties

1 Why poroelastic materials?

2 Why anisotropy?

3 Which properties?

4 How?

5 Summary

4 / 28


Why anisotropy?

Which properties?

How?

Summary




2 Why anisotropy?

3 Which properties?

4 How?

5 Summary

5 / 28


Why anisotropy?

Which properties?

How?

Summary

Why poroelastic materials?Challenges for the transport industry

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 201060

70

80

90

100

110

120

130

Year

Nor

mal

ised

CO

2em

issi

ons

EU

−27

TotalEnergy excl. transportTransportAgricultureIndustry (processes)Waste

Source: Eurostat

Increase energy efficiencyreduce structural massexpand load capacityminimise aerodynamic loadselectrical engines

6 / 28


Why anisotropy?

Which properties?

How?

Summary

Why poroelastic materials?Need for multifunctional designs

Courtesy of David Wennberg

7 / 28


Why anisotropy?

Which properties?

How?

Summary

Why poroelastic materials?Poroelastic materials in multifunctional designs

Poroelastic materialslightweight: > 95% air, < 5% solidmay have good acoustic insulation propertiesmay be fire resistantmay have good thermal insulation properties

8 / 28


Why anisotropy?

Which properties?

How?

Summary




2 Why anisotropy?

3 Which properties?

4 How?

5 Summary

9 / 28


Why anisotropy?

Which properties?

How?

Summary

Why anisotropy?Material microstructure

Anisotropyvariation of properties with directioninduced by the production processmay have significant impact on performance

10 / 28


Why anisotropy?

Which properties?

How?

Summary

Why anisotropy?

Source: Dongda Polyurethane

Anisotropyvariation of properties with directioninduced by the production processmay have significant impact on performance

11 / 28


Why anisotropy?

Which properties?

How?

Summary




2 Why anisotropy?

3 Which properties?

4 How?

5 Summary

12 / 28


Why anisotropy?

Which properties?

How?

Summary

Which properties?

Improve vibro-acoustic performanceflow resistivityelasticity

13 / 28


Why anisotropy?

Which properties?

How?

Summary

Which properties?Flow resistivity

resistance to airflow through a material

accumulated measure for visco-acousticlosses

direct influence on acoustic behaviour

Measurementstandardised method

σst =p1 − p2

Vin · tassuming isotropy

14 / 28


Why anisotropy?

Which properties?

How?

Summary

Which properties?Elasticity

relation between deformationand force

may be important for thevibrational behaviour

Measurementno standardised measurementmethodmeasurement methods availablein literature1

(assume simplified anisotropy)

(1) material sample

(2-5) tranducers

1Applied Acoustics Volume 69, 1129 - 1140 (2008) – http://dx.doi.org/10.1016/j.apacoust.2007.11.00815 / 28


Why anisotropy?

Which properties?

How?Inverse estimationprocedure

Flow resistivity

Elasticity

Summary




2 Why anisotropy?

3 Which properties?

4 How?

5 Summary

16 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary

How?Inverse estimation procedure

Numerical modelgood representation ofexperimental set-upeasy and fast to solve

Experimental set-upisolate property tosimplify modellingsimple geometry

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Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary




2 Why anisotropy?

3 Which properties?

4 How?Inverse estimation procedureFlow resistivityElasticity

5 Summary

18 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary

How?Flow resistivity tensor

Experimental set-up15 pairs experimental dataVin & ∆p

19 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Numerical modelDarcy’s Law: −∇p = σv15 pairs numerical dataVin & ∆p

19 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Model parametersσ

σ =

σxx σxy σxz

σyy σyz

(sym) σzz

19 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Assumptionslinearity and homogeneitylaminar incompressible flow

19 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Contributions – Paper Averification of numerical procedureapplication to glass wool and melamine foamvalidation of method

19 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary




2 Why anisotropy?

3 Which properties?

4 How?Inverse estimation procedureFlow resistivityElasticity

5 Summary

20 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary

How?Elasticity

Anelasticitystress-strain relationship is time- and frequency-dependentas a result of the solid base material

21 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary

How?Elasticity

Young’s Modulus

102

103

104

1050

200

400

600

800

Frequency [Hz]

E(ω

) [k

Pa]

Loss factor

102

103

104

1050

0.5

1

1.5

Frequency [Hz]

η(ω

) [−

]

Contributions – Paper Bhigh accuracy measurementshigh accuracy numerical predictionsgood correlation achieved by accounting for anelasticity

22 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary

How?Dynamic Hooke’s tensor

Experimental set-upin vacuumexperimental dataain & a1,2,3,4

repeated in 3 directions23 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Numerical modelAugmented Hooke’s lawσi(ω) = Hij(ω)εj(ω)

Hij(ω) = H(0)ij + H∆

ij (ω)

numerical dataain & a1,2,3,4

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Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Model parameters

Hij(ω) = H(0)ij + H∆

ij (ω)

= H(0)ij (1 + z f (α, β, ω))

H(0)ij , α, β, z

H(0)=

C11 C12 C13 0 0 0

C22 C23 0 0 0C33 0 0 0

C44 0 0(sym) C55 0

C66

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Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Assumptionslinearity and homogeneity

H(0)ij and H∆

ij collineargeneral orthotropy

23 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Contributions – paper Clinearity and repeatability of measurementsperform measurements on melamine foamgeneral orthotropic model

23 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Resultscorrelation between experimental and numerical data foroptimal solution

– : experimental data– : numerical data

Modulus of transfer functions Phase of transfer functions

Φ[u1]

100 200 300 400

f (Hz)

x

y

zπ

|u1|

100 200 300 400

f (Hz)

x

y

z× 10

24 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Results

modulus of Hooke’s matrix for optimal solution

|H(ω)| = 105

8.5

9.5

10−2 104 1010

3.8

4.2

10−2 104 1010

0.0240.0260.028

10−2 104 1010

3.8

4.2

10−2 104 1010

4.65

5.4

10−2 104 1010

1.3

1.5

10−2 104 1010

0.0240.0260.028

10−2 104 1010

1.3

1.5

10−2 104 1010

2.5

2.8

10−2 104 1010

1.11.21.3

10−2 104 1010

1.31.41.5

10−2 104 1010

1.11.21.3

10−2 104 1010

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary

How?Static Hooke’s tensor

Experimental set-uprepeated in 3 directionsexperimental dataui & F

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Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Numerical modelHooke’s Law:σi(0) = H(0)

ij εj(0)

numerical dataui & F

25 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Model parameters

H(0)ij ,EBC, νBC

H(0)=

C11 C12 C13 0 0 0

C22 C23 0 0 0C33 0 0 0

C44 0 0(sym) C55 0

C66

25 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Assumptionslinearity and homogeneityfully relaxed stategeneral orthotropyisotropic boundary layer

25 / 28


Why anisotropy?

Which properties?


Flow resistivity

Elasticity

Summary


Contributions – Papers D and Eimplementation of inverse estimation proceduregeneral orthotropic model and isotropic boundary layerverification of numerical procedureapplication to melamine foam

25 / 28


Why anisotropy?

Which properties?

How?

Summary




2 Why anisotropy?

3 Which properties?

4 How?

5 Summary

26 / 28


Why anisotropy?

Which properties?

How?

Summary

SummaryVibro-acoustic Modelling of Anisotropic Poroelastic Materials


Conclusionsprocedure of inverse estimation consisting of

controllable measurement set-upmodel governing involved physicsnumerical and optimisation tools

to characterise properties controlling the vibro-acousticbehaviour

flow resistivityelasticity

applied to melamine foamanisotropy and anelasticity are very relevant in poroelasticmaterialsproduction process has an important influence on materialproperties

27 / 28


Why anisotropy?

Which properties?

How?

Summary

SummaryVibro-acoustic Modelling of Anisotropic Poroelastic Materials


Future work and opportunitiescombination of dynamic and static characterisation method

further validation of the developed characterisationmethods

investigation of the boundary layer at materialdiscontinuities

study the influence of anisotropy on overall performance

control the foam engineering chainFoam chemistry - Foam processing - Foam cellmicromechanics - Macroscopic static & dynamicproperties - End application performance

27 / 28

Thank you

Christophe Van der Kelen

Ph.D. defenseJanuary 20, 2014, Stockholm, Sweden

SupervisorsProf. Peter Göransson

Prof. Wim Desmet

vibro-acoustic modelling of anisotropic poroelastic materials – characterisation of the...

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