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Shock and Vibration
Volume 17 (2010), Issue 4-5, Pages 429-444

Stochastic Modeling of Surface Viscoelastic Treatments Combined with Model Condensation Procedures

A.M.G. de Lima,1 D.A. Rade,1 and N. Bouhaddi2

1Federal University of Uberlândia – School of Mechanical Engineering, Campus Santa Mônica, P.O.Box 593, CEP 38400-902, Uberlândia-MG, Brazil
2University of Franche-Comtê, FEMTO-ST UMR 6174, Applied Mechanics Laboratory, 24 Chemin de l'Epitaphe, 25000, Besançon, France

Received 17 June 2010; Accepted 17 June 2010

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Engineering structures incorporating viscoelastic materials are characterized by inherent uncertainties affecting the parameters that control the efficiency of the viscoelastic dampers. In this context, the handling of variability in viscoelastic systems is a natural and necessary extension of the modeling capability of the present techniques of deterministic analysis. Among the various methods devised for uncertainty modeling, the stochastic finite element method has received major attention, as it is well adapted for applications to complex engineering systems. In this paper, the stochastic finite element method applied to a structural three-layer sandwich plate finite element containing a viscoelastic layer, with random parameters modelled as random fields, is presented. Accounting for the dependence of the behaviour of the viscoelastic materials with respect to frequency and temperature, using the concepts of complex modulus and shift factor, the uncertainties are modelled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method, using Karhunen-Loève expansions. The modeling procedure is confined to the frequency domain, and the dynamic responses are characterized by frequency response functions (FRF's). Monte Carlo Simulation (MCS) combined with Latin Hypercube Sampling is used as the stochastic solver. The typically high dimensions of finite element models of viscoelastic systems combined with the large number of Monte Carlo samples to be computed make the evaluation of the FRF's variability computer intensive. Those difficulties motivate the use of condensation methods specially adapted for viscoelastic systems, in order to alleviate the computational cost. After the presentation of the underlying formulation, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features and, particularly, the computation cost savings provided by the association of MCS with the suggested condensation procedure.