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International audienceThe effective design of viscoelastic dampers as applied to real-world complex engineering structures can be conveniently carried out by using modern numerical optimization and/or model updating techniques. However, the large number of exact evaluations of the cost functions, combined with the typically high dimensions of large finite element models of industrial structures incorporating viscoelastic materials, makes the numerical processes very costly, sometimes unfeasible. Those difficulties motivate the study reported herein, in which a general strategy to improve the standard condensation methods by taking into account a priori information of the modifications into the viscoelastic zones is introduced. The proposed method can be used with any condensation procedure, including direct reductions and component mode synthesis

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Flexible rotors are characterized by inherent uncertainties affecting the parameters that influence the dynamic responses of the system. In this context, the handling of variability in rotor dynamics is a natural and necessary extension of the modeling capability of the existing techniques of deterministic analysis. Among the various methods used to model uncertainties, the stochastic finite element method has received major attention, as it is well adapted for applications involving complex engineering systems of industrial interest. In the present contribution, the stochastic finite element method applied to a flexible rotor system, with random parameters modeled as random fields is presented. The uncertainties are modeled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method by using Karhunen-Loève expansions. The modeling procedure is confined to the frequency and time domain analyses, in which the envelopes of frequency response functions, the Campbell's diagram and the orbits of the stochastic flexible rotor system are generated. Also, Monte Carlo simulation method combined with the Latin Hypercube sampling is used as stochastic solver. After the presentation of the underlying theoretical formulations, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features of the stochastic modeling procedure of flexible rotor systems.

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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.