In this paper, linear viscoelastic rheological properties of acoustical damping materials are predicted. A rheological model, based on a mechanical element approach, is presented. It consists of a combination of two springs, two parabolic elements, and one dashpot (2S2P1D). This model is applied to different acoustical damping materials. Its specificity comes from the fact that elements might be linked to structural and physical features. Parameters might be experimentally determined by tests. Application of the 2S2P1D linear viscoelastic model can adequately predict the behavior of acoustical damping materials with good accuracy. If the material verifies the time–temperature superposition principle (TTSP), the proposed model can predict the behavior on a wide frequency range, even with a small number of available data.
Issue Section:
Research Papers
References
1.
Zwikker
, C.
, and Kosten
, C.
, 1949
, Sound Absorbing Materials
, Elsevier
, Amsterdam
.2.
Allard
, J.
, 1993
, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
, Elsevier
, Essex, UK
.3.
Olny
, X.
, Sgard
, F.
, Perrot
, C.
, and Panneton
, R.
, 2004
, “Microscopic and Mesoscopic Approaches for Describing and Building Sound Absorbing Porous Materials
,” Proceedings of the Second TUL-ENTPE Workshop
, Szklarska Poreba, Poland, Mar. 3–6, pp. 187
–206
.4.
Lind-Nordgren
, E.
, and Gransson
, P.
, 2010
, “Optimising Open Porous Foam for Acoustical and Vibrational Performance
,” J. Sound Vib.
, 329
(7
), pp. 753
–767
.10.1016/j.jsv.2009.10.0095.
Gourdon
, E.
, and Seppi
, M.
, 2010
, “Extension of Double Porosity Model to Porous Materials Containing Specific Porous Inclusions
,” Acta Acust. Acust.
, 96
(2
), pp. 275
–291
.10.3813/AAA.9182776.
Biot
, M.
, 1956
, “The Theory of Propagation of Elastic Waves in a Fluidsatured Porous Solid. I. Low Frequency Range
,” J. Acoust. Soc. Am.
, 28
(2
), pp. 168
–191
.10.1121/1.19082397.
Biot
, M.
, 1956
, “The Theory of Propagation of Elastic Waves in a Fluidsatured Porous Solid. II. Higher Frequency Range
,” J. Acoust. Soc. Am.
, 28
(2
), pp. 168
–191
.10.1121/1.19082398.
Capps
, R.
, 1983
, “Dynamic Young's Moduli of Some Commercially Available Polyurethanes
,” J. Acoust. Soc. Am.
, 73
(6
), pp. 2000
–2005
.10.1121/1.3895669.
Oyadiji
, S.
, and Tomlimson
, G.
, 1985
, “Determination of the Complex Moduli of Viscoelastic Structural Elements by Resonance and Non-Resonance Techniques
,” J. Sound Vib.
, 101
(3
), pp. 277
–298
.10.1016/S0022-460X(85)80129-210.
Corsaro
, R.
, and Sperling
, L.
, 1990
, Sound and Vibration Damping With Polymers
, American Chemical Society
, Washington, DC
.11.
Pritz
, T.
, 1994
, “Dynamic Young's Modulus and Loss Factor of Plastic Foams for Impact Sound Isolation
,” J. Sound Vib.
, 178
(3
), pp. 315
–322
.10.1006/jsvi.1994.148812.
Mariez
, E.
, Sahraoui
, S.
, and Allard
, J.
, 1996
, “Elastic Constants of Polyurethane Foams Skeleton for Biot Model
,” 25th International Congress on Noise Control Engineering
(Inter-Noise 96), Liverpool, UK, July 30–Aug. 2, pp. 951
–954
.13.
Dauchez
, N.
, Etchessahar
, M.
, and Sahraoui
, S.
, 2002
, “On Measurements of Mechanical Properties of Sound Absorbing Materials
,” Second Biot Conference on Poromechanics
, Grenoble, France, Aug. 26–28, pp. 627
–632
.14.
Pritz
, T.
, 1990
, “Non-Linearity of Frame Dynamic Characteristics of Mineral and Glass Wool Materials
,” J. Sound Vib.
, 136
(2
), pp. 263
–274
.10.1016/0022-460X(90)90855-T15.
Panneton
, R.
, and Langlois
, C.
, 2001
, “Polynomial Relation for the Mechanical Characterization of Poroelastic Materials
,” 17th International Congress of Acoustics (ICA '01), Rome, Italy, Sept. 2–7, Paper No. 4A.08.06.16.
Etchessahar
, M.
, Sahraoui
, S.
, Benyahia
, L.
, and Tassin
, J.
, 2005
, “Frequency Dependence of Elastic Properties of Acoustic Foams
,” J. Acoust. Soc. Am.
, 117
(1
), pp. 1114
–1121
.10.1121/1.185752717.
Van der Poel
, C.
, 1954
, “A General System Describing the Viscoelastic Properties of Bitumens and Its Relation to Routinr Test Data
,” J. Appl. Chem.
, 4
(5
), pp. 231
–236
.10.1002/jctb.501004050118.
Heukolem
, W.
, and Klomp
, J.
, 1964
, “Road Design and Dynamic Loading
,” Proceedings of the Association of Asphalt Paving Technologists
, Ann Arbor, MI, Vol. 33
, pp. 92
–125
.19.
Sayegh
, G.
, 1967
, “Viscoelastic Properties of Bituminous Mixtures
,” Second International Conference on Structural Design of Asphalt Pavement
, Ann Arbor, MI, pp. 743
–755
.20.
Havriliak
, S.
, and Negami
, S.
, 1967
, “A Complex Plane Representation of Dielectric and Mechanical Relaxation Processes in Some Polymers
,” Polymer
, 8
, pp. 161
–210
.10.1016/0032-3861(67)90021-321.
Hartmann
, B.
, Lee
, G. F.
, and Lee
, J.
, 1994
, “Loss Factor Height and Width Limits for Polymer Relaxations
,” J. Acoust. Soc. Am.
, 95
(1
), pp. 226
–233
.10.1121/1.40835522.
Pritz
, T.
, 2003
, “Five-Parameter Fractional Derivative Model for Polymeric Damping Materials
,” J. Sound Vib.
, 265
(5
), pp. 935
–952
.10.1016/S0022-460X(02)01530-423.
Kim
, S.-Y.
, and Lee
, D.-H.
, 2009
, “Identification of Fractional-Derivative-Model Parameters of Viscoelastic Materials From Measured Frfs
,” J. Sound Vib.
, 324
(3–5
), pp. 570
–586
.10.1016/j.jsv.2009.02.04024.
ASTM
, 2010
, “Standard Test Method for Measuring Vibration-Damping Properties of Materials,” ASTM International, West Conshohocken, PA, ASTM
Standard E756-05(2010).10.1520/E0756-05R1025.
Jones
, D.
, 2001
, Handbook of Viscoelastic Vibration Damping
, Wiley
, New York
.26.
Deng
, R.
, Davies
, P.
, and Bajaj
, A.
, 2003
, “Flexible Polyurethane Foam Modeling and Identification of Viscoelastic Parameters for Automotive Seating Applications
,” J. Sound Vib.
, 262
(3
), pp. 391
–417
.10.1016/S0022-460X(03)00104-427.
Kim
, S.-Y.
, and Lee
, D.-H.
, 2009
, “Identification of Fractional-Derivative-Model Parameters of Viscoelastic Materials From Measured FRFs
,” J. Sound Vib.
, 324
(3–5
), pp. 570
–586
.10.1016/j.jsv.2009.02.04028.
Olard
, F.
, and Di Benedetto
, H.
, 2003
, “General ‘2S2P1D’ Model and Relation Between the Linear Viscoelastic Behaviours of Bituminous Binders and Mixes
,” Road Mater. Pavement Des.
, 4
(2
), pp. 185
–224
.10.3166/rmpd.4.185-22429.
Olard
, F.
, Di Benedetto
, H.
, and Vaniscote
, J.-C.
, 2005
, “Properties of Bituminous Mixtures at Low Temperatures and Relations With Binder Characteristics
,” Mater. Struct.
, 38
(1
), pp. 121
–126
.10.1007/BF0248058430.
Di Benedetto
, H.
, Olard
, F.
, Sauzéat
, C.
, and Delaporte
, B.
, 2004
, “Linear Viscoelastic Behaviour of Bituminous Materials: From Binders to Mixes
,” Road Mater. Pavement Des.
, 5
(Suppl. 1
), pp. 163
–202
.10.1080/14680629.2004.968999231.
Di Benedetto
, H.
, Neifar
, M.
, Sauzéat
, C.
, and Olard
, F.
, 2007
, “Three-Dimensional Thermo-Viscoplastic Behaviour of Bituminous Materials: The DBN Model
,” Road Mater. Pavement Des.
, 8
(2
), pp. 285
–316
.10.3166/RMPD.8.285-31532.
Yin
, H.
, Buttlar
, W.
, Paulino
, G.
, and Di Benedetto
, H.
, 2008
, “Assessment of Existing Micro-Mechanical Models for Asphalt Mastics Considering Viscoelastic Effects
,” Road Mater. Pavement Des.
, 9
(1
), pp. 31
–57
.10.1080/14680629.2008.969010633.
Delaporte
, B.
, Di Benedetto
, H.
, Chaverot
, P.
, and Gauthier
, G.
, 2009
, “Linear Viscoelastic Properties of Bituminous Materials Including New Products Made With Ultrafine Particles
,” Road Mater. Pavement Des.
, 10
(1
), pp. 7
–38
.10.1080/14680629.2009.969018034.
Izzi
, Y. M. N.
, Mounier
, D.
, Ginoux
, M.
, Mohd
, H.
, Airey
, G.
, and Di Benedetto
, H.
, 2013
, “Modelling the Rheological Properties of Bituminous Binders Using the 2S2P1D Model
,” Constr. Build. Mater.
, 38
, pp. 395
–406
.10.1016/j.conbuildmat.2012.08.03835.
Mangiafico
, S.
, Di Benedetto
, H.
, Sauzéat
, C.
, Olard
, F.
, Pouget
, S.
, and Planque
, L.
, 2014
, “New Method to Obtain Viscoelastic Properties of Bituminen Blends From Pure and Rap Binder Constituents
,” Road Mater. Pavement Des.
, 15
(2
), pp. 312
–329
.10.1080/14680629.2013.87063936.
Tapsoba
, N.
, Sauzéat
, C.
, Di Benedetto
, H.
, Baaj
, H.
, and Ech
, M.
, 2014
, “Behavior of Asphalt Mixtures Containing Rap and Shingles
,” Road Mater. Pavement Des.
, 15
(2
), pp. 330
–347
.10.1080/14680629.2013.87109137.
Tiouajni
, S.
, Di Benedetto
, H.
, Sauzéat
, C.
, and Pouget
, S.
, 2011
, “Approximation of Linear Viscoelastic Model by Generalized Kelvin Voigt or Generalized Maxwell Models: Application to Bituminous Materials in the 3 Dimensional Case
,” Road Mater. Pavement Des.
, 12
(4
), pp. 897
–719
.10.1080/14680629.2011.971389938.
Fowler
, B.
, 1989
, “Interactive Characterization and Data Base Storage of Complex Modulus Data
,” Proceedings of Damping '89, West Palm Beach, FL, Feb. 8–10, Vol. 2, Paper No. FAA.39.
Deverge
, M.
, Benyahia
, L.
, and Sahraoui
, S.
, 2009
, “Experimental Investigation on Pore Size Effect on the Linear Viscoelastic Properties of Acoustic Foams
,” J. Acoust. Soc. Am.
, 126
(3
), pp. 93
–96
.10.1121/1.318679940.
Wojtowicki
, J.-L.
, Jaouen
, L.
, and Panneton
, R.
, 2004
, “New Approach for the Measurement of Damping Properties of Materials Using the Oberst Beam
,” Rev. Sci. Instrum.
, 75
(8
), pp. 2569
–2574
.10.1063/1.177738241.
Williams
, M.
, Landel
, R.
, and Ferry
, J.
, 1955
, “The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glassforming Liquids
,” J. Am. Chem. Soc.
, 77
(14
), pp. 3701
–3707
.10.1021/ja01619a00842.
Booij
, H.
, and Thoone
, G.
, 1982
, “Generalization of Kramerskronig Transforms and Some Approximations of Relations Between Viscoelastic Quantities
,” Rheol. Acta
, 21
(1
), pp. 15
–24
.10.1007/BF0152070143.
Gergesova
, M.
, Zupancic
, B.
, Saprunov
, I.
, and Emri
, I.
, 2011
, “The Closed Form t-T-P Shifting (CFS) Algorithm
,” J. Rheol.
, 55
(1
), pp. 1
–16
.10.1122/1.350352944.
Madigosky
, W.
, Lee
, G.
, and Niemiec
, J.
, 2006
, “A Method for Modeling Polymer Viscoelastic Data and the Temperature Shift Function
,” J. Acoust. Soc. Am.
, 119
(6
), pp. 3760
–3765
.10.1121/1.219529245.
Guedes
, R.
, 2011
, “A Viscoelastic Model for a Biomedical Ultra-High Molecular Weight Polyethylene Using the Time-Temperature Superposition Principle
,” Polym. Test.
, 30
(3
), pp. 294
–302
.10.1016/j.polymertesting.2011.01.00646.
Rouleau
, L.
, Deu
, J.-F.
, Legay
, A.
, and Lay
, F. L.
, 2013
, “Application of Kramers–Kronig Relations to Time-Temperature Superposition for Viscoelastic Materials
,” Mech. Mater.
, 65
, pp. 66
–75
.10.1016/j.mechmat.2013.06.00147.
Pritz
, T.
, 1999
, “Verification of Local Kramers–Kronig Relations for Complex Modulus by Means of Fractional Derivative Model
,” J. Sound Vib.
, 228
(5
), pp. 1145
–1165
.10.1006/jsvi.1999.249548.
Di Benedetto
, H.
, Sauzéat
, C.
, and Sohm
, J.
, 2009
, “Stiffness of Bituminous Mixtures Using Ultrasonic Waves Propagation
,” Road Mater. Pavement Des.
, 10
(4
), pp. 789
–814
.10.1080/14680629.2009.969022749.
Mounier
, D.
, Di Benedetto
, H.
, and Sauzéat
, C.
, 2012
, “Determination of Bituminous Mixtures Linear Properties Using Ultrasonic Wave Propagation
,” Constr. Build. Mater.
, 36
, pp. 638
–647
.10.1016/j.conbuildmat.2012.04.13650.
Gudmarsson
, A.
, Ryden
, N.
, Di Benedetto
, H.
, Sauzéat
, C.
, Tapsoba
, N.
, and Birgisson
, B.
, 2014
, “Comparing Linear Viscoelastic Properties of Asphalt Concrete Measured by Laboratory Seismic and Tension-Compression Tests
,” J. Nondestr. Eval.
, 33
(4
), pp. 571
–582
.10.1007/s10921-014-0253-951.
Levenberg
, K.
, 1944
, “A Method for the Solution of Certain Problems in Least-Squares
,” Q. Appl. Math.
, 2
, pp. 164
–168
.52.
Marquardt
, D.
, 1963
, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,” SIAM J. Appl. Math.
, 11
(2
), pp. 431
–441
.10.1137/011103053.
Moré
, J.
, 1977
, “The Levenberg–Marquardt Algorithm: Implementation and Theory
,” Numerical Analysis
(Lecture Notes in Mathematics, Vol. 630), G. A.
Watson
, ed., Springer-Verlag
, Heidelberg, Germany
, pp. 105
–116
.10.1007/BFb006770054.
Gauthier
, P.
, and Rivaille
, P.-Y. H.
, 2009
, “Fitting the Smile, Smart Parameters for SABR and Heston
,” Social Science Research Network, Rochester, NY.10.1520/E0756-05R10Copyright © 2015 by ASME
You do not currently have access to this content.
