Robust design of viscoelastic structures based on stochastic finite element models

In this paper, a methodology of uncertainty propagation is investigated as related to constrained viscoelastic layers in the context of passive vibration damping. The uncertainties are introduced on multilayer beam and plate finite elements by means of an original strategy, which consists in introducing the perturbations after an adequate parameterisation of the mass and complex stiffness matrices. Such parameterisation scheme enables to perform iterative model updating, sensitivity analyses and uncertainty propagation analyses at a moderate computational cost since re-actualisation of the nominal global finite element matrices is not required. The design space is composed by both the parameters characterising the viscoelastic treatment and those of the base structure. The theoretical foundations related to the modelling of viscoelastic systems and stochastic finite element models are first reviewed, followed by a description of the parameterisation technique. Finally, numerical applications are presented to demonstrate the effectiveness of the proposed strategy for the robust design of structures incorporating viscoelastic materials.