Affiliations: Federal University of Uberlândia – School of Mechanical Engineering, Campus
Santa Mônica, P.O.Box 593, CEP 38400-902, Uberlândia-MG, Brazil | University of Franche-Comtê, FEMTO-ST UMR 6174,
Applied Mechanics Laboratory, 24 Chemin de l'Epitaphe, 25000, Besançon,
France
Abstract: 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.
Keywords: Uncertainty propagation, viscoelasticity, model condensation, stochastic finite elements
