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Research Papers

Seven-Parameter Linear Viscoelastic Model Applied to Acoustical Damping Materials

[+] Author and Article Information
E. Gourdon

Ecole Nationale des Travaux Publics de l'Etat,
LGCB, LTDS UMR CNRS 5513,
Rue Maurice Audin,
Vaulx en Velin Cedex 69518, France
e-mail: emmanuel.gourdon@entpe.fr

C. Sauzéat, H. Di Benedetto

Ecole Nationale des Travaux Publics de l'Etat,
LGCB, LTDS UMR CNRS 5513,
Rue Maurice Audin,
Vaulx en Velin Cedex 69518, France

K. Bilodeau

Bauval, 3550 Butte-aux-Renards,
Varennes, QC J3X 1P7, Canada

1Corresponding author.

2Former affiliation: Laboratoire Génie Civil et Bâtiment and LTDS UMR CNRS 5513, ENTPE, Rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, France, and EIFFAGE Travaux Publics, R&D Dept., 8 rue du Dauphiné CS 74005, 69964 Corbas, France.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 28, 2014; final manuscript received April 14, 2015; published online July 9, 2015. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 137(6), 061003 (Dec 01, 2015) (9 pages) Paper No: VIB-14-1452; doi: 10.1115/1.4030719 History: Received November 28, 2014; Revised April 14, 2015; Online July 09, 2015

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.

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References

Figures

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Fig. 1

Mechanical representation of the fractional Zener model

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Fig. 2

Mechanical representation of the five-parameter fractional-derivative model

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Fig. 3

Mechanical representation of the 2S2P1D model. h and k are the two parabolic creep elements.

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Fig. 7

Cyclic shear properties of a polyurethane foam: (a) master curve of norm of G* (in Pa); (b) master curve of phase angle of G* (in degree); (c) complex modulus (in Pa) in Cole–Cole axes; and (d) complex modulus (in Pa) in black space. The gray continuous line represents the 2S2P1D model, the gray dashed line represents the five-parameter fractional-derivative model, and the diamonds represent experimental measurements (Tref = +10 °C).

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Fig. 8

Young's modulus properties of a polyvinyl chloride-based viscoelastic material: (a) norm of E* (in Pa) for six isotherms and (b) phase angle (in degree) of E* for six isotherms

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Fig. 9

Young's modulus properties of a polyvinyl chloride-based viscoelastic material: (a) master curve of norm of E* (in Pa); (b) master curve of phase angle of E* (in degree); (c) complex modulus (in Pa) in Cole–Cole axes; and (d) complex modulus (in Pa) in black space. The gray continuous line represents the 2S2P1D model, the gray dashed line represents the five-parameter fractional-derivative model, and the diamonds represent experimental measurements (Tref = +5 °C).

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Fig. 6

Cyclic shear properties of a polyurethane foam: (a) norm of G* (in Pa) for six isotherms and (b) phase angle (in degree) of G* for six isotherms

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Fig. 5

Cyclic shear properties of a polymeric damping material: (a) master curve of norm of G* (in Pa); (b) master curve of phase angle of G* (in degree); (c) complex modulus (in Pa) in Cole–Cole axes; and (d) complex modulus (in Pa) in black space. The gray continuous line represents the 2S2P1D model, the gray dashed line represents the five-parameter fractional-derivative model, and the diamonds represent experimental measurements.

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Fig. 4

Complex modulus in Cole–Cole axes

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