Wide estimation of dynamic properties of viscoelastic materials using Bayesian inference
More details
Hide details
Federal University of Paraná, Postgraduate Program in Mechanical Engineering, Curitiba, Brazil
Federal University of Paraná, Postgraduate Program in Engineering and Science of Materials, Curitiba, Brazil
Federal University of Paraná, Department of Statistics, Curitiba, Brazil
Submission date: 2020-11-30
Acceptance date: 2021-03-29
Online publication date: 2021-05-29
Publication date: 2021-07-25
Journal of Theoretical and Applied Mechanics 2021;59(3):369-384
The dynamic behavior of a typical viscoelastic material in wide ranges of frequency and tem- perature is characterized. A four-parameter fractional derivative model was considered in the frequency domain along with the Arrhenius and WLF models, also for including tempera- ture as a source of variation. A Bayesian framework is adopted and inferences on parameters governing the model quantities of interest are based on samples from posterior distributions obtained by Monte Carlo Markov Chain (MCMC) methods. Posterior predictive checks were conducted to ensure the goodness-of-fit of the model. Based on the results we argue that the Bayesian framework allows more complete and suitable inference about dynamic properties of typical viscoelastic materials, as required for broad and sound vibration control actions.
Bagley R.L., Torvik P.J., 1986, On the fractional calculus model of viscoelastic behavior, Journal of Rheology, 30, 133-156.
Balbino F.O., 2012, Statistical Analysis of Experimental Data on Dynamic Characterization of Viscoelastic Materials (in Portuguese), Master’s Dissertation, Federal University of Paraná, Paraná, Brazil (available at 047 Fernanda-Oliveira-Balbino.pdf).
Gamerman D., Lopes H.F., 2006, Markov Chain Monte Carlo, 2nd ed., Chapman & Hall.
Gelman A., 2003, Bayesian formulation of exploratory data analysis and goodness-of-fit testing, International Statistical Review, 71, 2, 369-382.
Gelman A., Rubin D.B., 1992, Inference from iterative simulation using multiple sequences, Statistical Science, 7, 4, 457-511.
Gogu C., Haftka R., Le Riche R., Molimard L., Vautrin A., 2010, Introduction to the Bayesian approach applied to elastic constant identification, AIAA Journal, 48, 5, 893-903.
Hernández W.P., Castello D.A., Roitman N., Magluta C., 2017, Thermorheologically simple materials: a Bayesian framework for model calibration and validation, Journal of Sound and Vibration, 402, 14-30.
Hilton H.H., 2003, Optimum viscoelastic designer materials for minimizing failure probabilities during composite curing, Journal of Thermal Stresses, 26, 547-557.
Jones D.I.G., 1992, Results of a round Robin test program: complex modulus properties of a polymeric damping material, Final Report for Period Oct 1986-May 1992, WL-TR-92-3104,Wright Laboratory, Flight Dynamics Directorate, Structural Dynamics Branch, Wright-Patterson AFB, Ohio, USA.
Jones D.I.G., 2001, Handbook of Viscoelastic Vibration Damping, John Wiley & Sons.
Kruschke J.K., 2015, Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, 2nd ed., Elsevier.
Lopes E.M.O., 1998, On the Experimental Response Reanalysis of Structures with Elastomeric Materials, PhD Thesis, University of Wales, Cardiff, United Kingdom (available on request from either Arts and Social Studies Library, Cardiff University, or the last author).
Mead D.J., 1999, Passive Vibration Control, John Wiley & Sons.
Medeiros W.B.J., Préve C.T., Balbino F.O., da Silva T.A., Lopes E.M.O., 2019, On an integrated dynamic characterization of viscoelastic materials by fractional derivative and GHM models, Latin American Journal of Solids and Structures, 16, 1-19.
Migon H.S., Gamerman D., Louzada F., 2015, Statistical Inference: An Integrated Approach, 2nd ed., CRC Press.
Nashif A.D., Jones D.I.G., Henderson J.P., 1985, Vibration Damping, John Wiley & Sons.
Netzsch, 2015, Dynamic-Mechanical Analysis DMA 242 C (available at, accessed on 20 Feb 2021).
Plummer M., 2003, JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling, Proceedings of the 3rd International Workshop on Distributed Statistical Computing, Vienna, Austria, 124, 125.10, 1-10.
Plummer M., 2014, RJAGS: Bayesian Graphical Models Using MCMC, R package version 3-14,
Préve C.T., Balbino F.O., Ribeiro Jr. P.J., Lopes E.M.O., 2021, On the use of viscoelastic materials characterized by Bayesian inference in vibration control, Journal of Theoretical and Applied Mechanics, 59, 3, 385-399.
Pritz T., 1996, Analysis of four-parameter fractional derivative model of real solid materials, Journal of Sound and Vibration, 195, 103-115.
R Core Team, 2015, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria.
Scherbakov M., Gurvich M.R., 2005, Probabilistic modeling of hysteretic behavior of elastomers under 3-D cyclic loading, Journal of Elastomers and Plastics, 37, 2, 123-147.
Sousa T.L. de, Kanke F., Pereira J.T., Bavastri C.A., 2017, Property identification of viscoelastic solid materials in nomograms using optimization techniques, Journal of Theoretical and Applied Mechanics, 55, 1285-1297.
Zhang E., Chazot J.D., Antoni J., Hamdi M., 2013, Bayesian characterization of Young’s modulus of viscoelastic materials in laminated structures, Journal of Sound and Vibration, 332, 3654-3666.
Journals System - logo
Scroll to top