Abstract
This chapter is devoted to the use of viscoelastic materials as a strategy intended for passive vibration control in mechanical systems. It provides a review of the theoretical foundations underlying the constitutive modeling of the viscoelastic behavior, and the association of constitutive models with modern numerical resolution procedures, especially the finite element method. This currently enables the accurate prediction of the dynamic behavior of rather complex structural systems featuring viscoelastic dampers, duly accounting for the particular characteristics of the viscoelastic behavior, namely the memory effect and the dependence of stiffness and damping properties on frequency and temperature. Other relevant aspects considered are: (i) model condensation techniques, intended to reduce the computation cost involved in the evaluation of the response of viscoelastic structures using finite element models with large numbers of degrees-of-freedom; (ii) the identification of viscoelastic constitutive models from experimental data. In addition, some applications of viscoelastic materials to structures of engineering interest are presented to illustrate the use of some techniques discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The Lamé coefficients can depend more generally on various parameters (see Sect. 5.2.1).
References
Rao, M.D.: Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes. In: USA Symposium on Emerging Trends in Vibration and Noise Engineering, India (2001)
Zhou, X.Q., Yu, D.Y., Shao, X.Y., Zhang, S.Q., Wang, S.: Research and applications of viscoelastic vibration damping materials: a review. Compos. Struct. 136, 460–480 (2016)
Nashif, A.D., Jones, D.I.G., Henderson, J.P.: Vibration Damping, p. 1985. Wiley, New York (1985)
Bobillot, A., Balmès, E.: Analysis and design tools for structures damped by viscoelastic materials. In: International Modal Analysis Conference—IMAC, Los Angeles (2002)
Christensen, R.M.: Theory of Viscoelasticity. Dover Publications, New York, NY (2003)
Guillot, F.M., Trivett, D.H.: Complete elastic characterization of viscoelastic materials by dynamic measurements of the complex bulk and Young’s moduli as a function of temperature and hydrostatic pressure. J. Sound Vib. 330, 3334–3351 (2011)
Pritz, T.: Measurement methods of complex Poisson’s ratio of viscoelastic materials. Appl. Acoust. 60, 279–292 (2000)
Kaliske, M., Rothert, H.: Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Comput. Mech. 19, 228–239 (1997)
Pritz, T.: Frequency dependences of complex moduli and complex Poisson’s ratio of real solid materials. J. Sound Vib. 214, 83–104 (1998)
Ferry, J.D.: Viscoelastic properties of polymers. John Wiley & Sons (1980)
Emri, I.: Rheology of solid polymers. Rheol. Rev. 3, 49–100 (2005)
Dealy, J., Plazek, D.: Time-temperature superposition - a users guide. Rheol. Bull. 78, 16–31 (2009)
Soovere J, Drake ML (1984) Aerospace structures technology damping design guide. Technology review, Technical report, DTIC Document, aFWAL-TR-84-3089, vol. I
Rouleau, L., Deü, J.-F., Legay, A., Le Lay, F.: Application of Kramers-Kronig relations to time-temperature superposition for viscoelastic materials. Mech. Mat. 65, 66–75 (2013)
Thorin, A., Azoug, A., Constantinescu, A.: Influence of prestrain on mechanical properties of highly-filled elastomers: measurements and modeling. Polym. Testing 31, 978–986 (2012)
Martinez-Agirre, M., Illescas, S., Elejabarrieta, M.J.: Characterisation and modelling of prestrained viscoelastic films. Int. J. Adh. Adhes. 50, 183–190 (2014)
Wineman, A.S., Rajagopal, K.R.: Mechanical Response of Polymers. Cambridge University Press, Cambridge (2000)
Lakes, R.S.: Viscoelastic Solids. CRC Press (1998)
Mainardi, F.: Fractional Calculus and Waves in Linear Viscoelasticity. Imperial College, London (2005)
Podlubny, I.: Fractional Differential Equations. Academic Press (1999)
Yin, D., Duan, X., Zhou, X., Li, Y.: Time-based fractional longitudinal-transverse strain model for viscoelastic solids. Mech. Time-Depend. Mater. 18, 329–337 (2014)
Zhang, G., Yang, H., Xu, Y.: A surrogate-model-based identification of fractional viscoelastic constitutive parameters. Mech. Time-Depend. Mater. 1, 1–19 (2015)
Ghoreishy, M.H.R., Firouzbakht, M., Naderi, G.: Parameter determination and experimental verification of Bergström-Boyce hysteresis model for rubber compounds reinforced by carbon black blends. Mater. Design 53, 457–465 (2014)
Lion, A.: On the thermodynamics of fractional damping elements. Contin. Mech. Thermodyn. 9, 83–96 (1997)
Kaipio, J., Somersalo, E.: Statistical and Computational Inverse Problems, 1st edn. Springer, New York, NY (2005)
Aster, R.C., Borchers, C., Thurber, C.H.: Parameter Estimation and Inverse Problems, 2nd edn. Academic Press (2013)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis, 2nd edn. Chapman & Hall/CRC, Boca Raton, Florida (2004)
Melchers, R.E., Beck, A.T.: Structural Reliability Analysis and Prediction, 3rd edn. Wiley (2018)
Smith, R.C.: Uncertainty Quantification: Theory, Implementation, and Applications. SIAM, Computational Science and Engineering (2013)
Robert, C.P., Casella, G.: Monte Carlo Statistical Methods, 2nd edn. Springer, New York, NY (2010)
Gamermam, D., Lopes, H.F.: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd edn. Chapman and Hall/CRC (2006)
Hughes, T.J.R.: The Finite Element Method—Linear Static and Dynamic Finite Element Analysis. Prentice Hall Inc., Englewood Cliffs, N.J. (1987)
Khatua, T.P., Cheung, Y.K.: Bending and vibration of multilayer sandwich beams and plates. Int. J. Numer. Methods Eng. 6, 11–24 (1973)
Carrera, E.: Historical review of Zig-Zag theories for multilayered plates and shells. Appl. Mech. Rev. 56(3), 287–308 (2003)
Austin, E.M.: Variations on modeling of constrained-layer damping treatments. Shock Vib. Digest 31(4), 275–280 (1999)
Rouleau, L., Deü, J.-F., Legay, A.: A comparison of model reduction techniques based on modal projection for structures with frequency-dependent damping. Mech. Syst. Signal Pr. 90, 110–125 (2017)
Vasques, C., Moreira, R., Rodrigues, J.: Viscoelastic damping technologies—Part I: Modeling and finite element implementation. J. Adv. Res. Mech. Eng. 1, 76–95 (2010)
Antoulas, A.C.: Approximation of Large-Scale Dynamical Systems. Advances in Design and Control. SIAM, Philadelphia, PA, USA (2005)
Hetmaniuk, U., Tezaur, R., Farhat, C.: Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems. Int. J. Numer. Methods Eng. 90, 1636–1662 (2012)
Craig, R.R., Chang, C.-J.: A review of substructure coupling methods for dynamic analysis. Adv. Eng. Sci. 2, 393–408 (1976)
de Klerk, D., Rixen, D.J., Voormeeren, S.N.: General framework for dynamic substructuring: history, review and classification of techniques. AIAA J. (2008)
Balmès, E.: Parametric families of reduced finite element models. Mech. Syst. Signal Pr. 10, 381–394 (1996)
Balmès, E., Bobillot, A.: Analysis and design tool for structures damped by viscoelastic materials. In: Proceedings of the 21st ISMA Conference, Leuven, Belgium (2002)
Hu, B.-G., Dokaishi, M., Mansour, W.: A modified MSE method for viscoelastic systems: a weighted stiffness matrix approach. Trans. ASME J. Appl. Mech. 117, 226–231 (1995)
Johnson, C., Kienholz, D., Rogers, L.: Finite element prediction of damping in beams with constrained vicoelastic layers. Shock Vib. 1, 71–81 (1980)
Lin, R., Lim, M.: Complex eigensensitivity-based characterization of structures with viscoelastic damping. J. Acoust. Soc. Am. 100, 3182–3191 (1996)
Plouin, A.-S., Balmès, E.: Pseudo-modal representations of large models with viscoelastic behavior. In: Proceedings of the 16th ISMA Conference, Leuven, Belgium (1998)
Zhang, S., Chen, H.: A study on the damping characteristics of laminated composites with integral viscoelastic layers. Compos. Struct. 74, 63–69 (2006)
Dickens, J., Nakagawa, J., Wittbrodt, M.: A critique of mode acceleration and modal truncation augmentation methods for modal response analysis. Comput. Struct. (1997)
Tisseur, F., Meerbergen, K.: The quadratic eigenvalue problem. SIAM Rev. 43, 235–286 (2001)
Daya, E., Potier-Ferry, M.: A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures. Comput. Struct. 79 (2001)
Tran, G., Ouisse, M., Bouhaddi, N.: A robust component mode synthesis method for stochastic damped virboacoustics. Mech. Syst. Signal Pr. 24, 164–181 (2010)
de Lima, A., da Silva, A., Rade, D., Bouhaddi, N.: Component mode synthesis combining robust enriched Ritz approach for viscoelastically damped structures. Eng. Struct. (2010)
Baker, G.J., Graves-Moris, P.: Padé Approximants. Cambridge University Press (1996)
Avery, P., Farhat, C., Reese, G.: Fast frequency sweep computations using a multi-point Padé-based reconstruction method and an efficient iterative solver. Int. J. Numer. Methods Eng. 69, 2848–2875 (2007)
Chazot, J.-D., Nennig, B., Chettah, A.: Harmonicresponse computation of viscoelastic multilayered structures using a ZPST shell element. J. Sound Vib. 89, 2522–2530 (2011)
Rumpler, R., Göransson, P.: An assessment of two popular Padé-based approaches for fast frequency sweeps of time-harmonic finite element problems. In: Proceedings of Acoustics’17, Boston, USA (2017)
Millithaler, P., Dupont, J.-B., Ouisse, M., Sadoulet-Reboul, E., Bouhaddi, N.: VIscoelastic property tuning for reducing noise radiated by switched-reluctance machines. J. Sound Vib. 407, 191–208 (2017)
Hirsou, D., Le Quere, E., Magnier, M., Selosse, D.: Rotary electric machine, and in particular motor vehicle alternator, comprising a stator elastically mounted in a heat-conductive resin. European patent EP1249064B1 (2002)
Hernandéz, W.P., Castello, D.A., Roitman, N., Magluta, C.: Thermorheologically simple materials: a Bayesian framework for model calibration and validation. J. Sound Vib. 402(18), 14–30 (2017)
Borges, F.C.L., Castello, D.A., Magluta, C., Rochinha, F.A., Roitman, N.: An experimental assessment of internal variables constitutive models for viscoelastic materials. Mech. Syst. Signal Process. 50–51, 27–40 (2015)
Castello, D.A., Rochinha, F.A., Roitman, N., Magluta, C.: Constitutive parameter estimation of a viscoelastic model with internal variables. Mech. Syst. Signal Process. 22(8), 1840–1857 (2008)
Zhang, E., Chazot, J.D., Antoni, J., Hamdia, M.: Bayesian characterization of Young’s modulus of viscoelastic materials in laminated structures. J. Sound Vib. 332(16), 3654–3666 (2013)
Faming, L., Liu, C., Carroll, R.J.: Advanced Markov Chain Monte Carlo Methods—Learning from Past Samples. Wiley, Chichester, Wester Sussex (2010)
Wright, J.R., Cooper, J.E.: Introduction to Aeroelasticity and Loads, 2nd edn. Wiley (2015)
NASA: Control of Aeroelastic Response: Taming the Threats. NASA Historical Series 100 (2004)
Lacarbonara, W., Cetraro, M.: Flutter control of a lifting surface via visco-hysteretic vibration absorbers. Int. J. Aeronaut. Space Sci. 12, 331–345 (2011)
Merrett, C.G., Hilton, H.H.: Elastic and viscoelastic panel flutter in incompressible, subsonicandsupersonicflows. J. Aeroelast. Struct. Dyn. 2(2010), 53–80 (2010)
Cunha-Filho de Lima, A.M.G., Donadon, M.V., Leão, L.S.: Flutter suppression of plates using passive constrained viscoelastic layers. Mech. Syst. Signal Process. 79, 99–111 (2016)
Martins, P.C.O., DA Guimarães, Pereira, Marques, F.D., Rade, D.A.: Numerical and experimental investigation of aeroviscoelastic systems. Mech. Syst. Signal Process. 85, 680–697 (2017)
Cunha-Filho, A.G., Briend, Y.P.J., Lima, A.M.G., Donadon, M.V.: An efficient iterative model reduction method for aeroviscoelastic panel flutter analysis in the supersonic regime. Mech. Syst. Signal Process. 575–588 (2018)
de Lima, A.M.G., da Silva, A.R., Rade, D.A., Bouhaddi, N.: Component mode synthesis combining robust enriched Ritz approach for viscoelastically damped structures. Eng. Struct. 32, 1479–1488 (2010)
Bobillot, A., Balmés, A.: Iterative techniques for eigenvalue solutions of damped structures coupled with fluids. AIAA J. 32, 2002-1391 (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Rade, D.A., Deü, JF., Castello, D.A., de Lima, A.M.G., Rouleau, L. (2019). Passive Vibration Control Using Viscoelastic Materials. In: Jauregui, J. (eds) Nonlinear Structural Dynamics and Damping. Mechanisms and Machine Science, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-030-13317-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-13317-7_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13316-0
Online ISBN: 978-3-030-13317-7
eBook Packages: EngineeringEngineering (R0)