Validating the modeling of sandwich structures with constrained layer damping using fractional derivative models

  • R. Pirk
  • L. Rouleau
  • W. Desmet
  • B. Pluymers
Technical Paper


The effect of the damping insertion due to viscoelastic material (VEM) on the dynamic behavior of aluminum panels is assessed in this work. Dynamic mechanical analysis tests are carried out, aiming at characterizing the rheological behavior of a VEM compound. The time–temperature superposition principle is applied and the VEM compound master curve is built over a large frequency range. The parameters of the fractional derivative model are identified from the obtained master curve, and then input in the model. A distributed coating of constrained VEM applied to a homogeneous aluminum plate is considered in this study. In a first step, the responses of this sandwich structure are calculated by using finite element method (FEM). Free and clamped boundary conditions configurations are modeled. In a second step, tests are performed using the KULeuven test facilities by reproducing the same modeled configurations and the experimental frequency response functions (FRF) are measured. To validate the built FEM models, numerical vs. experimental FRF comparisons are done. Despite a slight underestimation of the damping, good agreements were observed in the whole frequency range.


Viscoelastic material Sandwich panel Constrained layer damping Fractional derivative model 



The Brazilian Science without Borders Program is acknowledged by the first author. The KU Leuven Research Fund, the European Marie Curie IAPP Project INTERACTIVE and the Strategic Initiative Materials in Flanders (SIM) through the “MacroModelMat,M3NVH” Program are also gratefully acknowledged for their support.


  1. 1.
    ASTM E-756 (2010) Standard test method for measuring vibration-damping properties of materials. ASTM International, West ConshohockenGoogle Scholar
  2. 2.
    Bendat JS, Piersol AG (1986) Random data, analysis and measurement procedures, 2nd edn. Wiley, USA. ISBN 0-471-04000-2 (Revised and Expanded) Google Scholar
  3. 3.
    Bert CW (1973) Material damping: an introductory review of mathematic measures and experimental techniques. J Sound Vib 29(2):129–153MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Chartoff R TA instruments, dynamic mechanical analyzers, rheology applications note. Application of time-temperature superposition principles to rheologyGoogle Scholar
  5. 5.
    Dealy J, Plazek D (2009) Time-temperature superposition—a users guide. Rheol Bull 78(2):16–31Google Scholar
  6. 6.
    Ewin DJ (1986) Modal testing: theory and practice (Mechanical Engineering Research Studies: Engineering Dynamics Series), 2nd edn. Research Studies Press Ltd., Brüel & Kjaer, England. ISBN 0-86380-036-XGoogle Scholar
  7. 7.
    Fahy F, Gardonio P (2007) Sound and structural vibration—radiation, transmission and response, 2nd edn., Institute of Sound and Vibration Research. Academic Press Inc., SouthamptonGoogle Scholar
  8. 8.
    Fowler B, Rogers L (2006) A new approach to the vertical shift of complex modulus data for damping polymers. In: Proceedings of the 77th shock and vibration symposium, Monterey, oct 29– nov 2 2006Google Scholar
  9. 9.
    Géradin M, Rixen DJ (2015) Mechanical vibrations—theory and application to structural dynamics, 3rd edn. Wiley, West SussexGoogle Scholar
  10. 10.
    Heylen W, Lammens S, Sas P (2013) Modal analysis theory and testing, Department of Mechanical Engineering, Faculty of Engineering, Katholieke Universiteit Leuven, Belgium. ISBN 90-73802-61-XGoogle Scholar
  11. 11.
    International Standard ISO (1996) ISO 6721-6—Plastics—determination of dynamic mechanical properties–part 6: shear vibration–Non-resonance methodGoogle Scholar
  12. 12.
    Le Rouzic J, Delobelle P, Vairac P, Cretin B (2009) Comparison of three different scales techniques for the dynamic mechanical characterization of two polymers (PDMS and SU8). Eur Phys J Appl Phys 48(1):1–14CrossRefGoogle Scholar
  13. 13.
    Leissa AW, Mohamad SQ (2011) Vibrations of continuous systems. McGraw-Hill Companies, Inc., USAGoogle Scholar
  14. 14.
    Lyon RH, DeJong RG (1995) Theory and application of statistical energy analysis, 2nd edn. Butterworth-Heinemann, USAGoogle Scholar
  15. 15.
    Nashif AD, Jones DIG, Henderson JP (1985) Vibration damping. Wiley, New YorkGoogle Scholar
  16. 16.
    Park SW (2001) Analytical modeling of viscoelastic dampers for structural and vibration control. Int J Solids Struct 38:8065–8092CrossRefMATHGoogle Scholar
  17. 17.
    Placet V, Foltête E (2010) Is dynamic mechanical analysis (DMA) a non-resonance technique? EPJ Web Conf 6:41004Google Scholar
  18. 18.
    Rouleau L (2013) Modélisation Vibro-acoustique de Structures Sandwich Munies de Matériaux Viscoélastiques, Thèse de Doctorat from Conservatoire National des Arts et Métiers, Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC), FranceGoogle Scholar
  19. 19.
    Rouleau L, Deü J-F, Legay A, Le Lay F (2013) Application of the Kramers-Kronig relations to time-temperature superposition principle for viscoelastic materials. Mech Mater 65:66–75CrossRefGoogle Scholar
  20. 20.
    Ungar EE (1962) Loss factors of viscoelastic systems in terms energy concepts. J Acoust Soc Am 34(7):954MathSciNetCrossRefGoogle Scholar
  21. 21.
    Vivolo M (2013) Vibro-acoustic characterization of lightweight panels by using a small cabin. Ph. D. Thesis, Department of Mechanical Engineering, Faculty of Engineering, Katholieke Universiteit LeuvenGoogle Scholar
  22. 22.
    Von Estorff O (2007) Boundary elements in acoustics: advances and applications (Applicable mathematics series). WIT Press, SouthamptonGoogle Scholar
  23. 23.
    Zienkiewicz OC, Taylor RL (2005) The finite element method—the three volume set, 6th edn. Butterworth-Heinemann, USAGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2016

Authors and Affiliations

  1. 1.KU Leuven, Department of Mechanical EngineeringHeverleeBelgium
  2. 2.Institute of Aeronautics and Space (IAE)/Technological Institute of Aeronautics (ITA)São José dos CamposBrazil
  3. 3.LMSSC, Conservatoire national des arts et métiersParisFrance

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