A ROBUST CONDENSATION STRATEGY FOR STOCHASTIC DYNAMIC SYSTEMS

Resumo

In traditional design of engineering systems, it is normally assumed the mean values of the physical and mechanical properties. However, in real-world applications it may not characterize with reasonable accuracy the modifications on the dynamic behavior of the resulting systems induced by small changes on their design variables. Thus, it is interesting to perform a stochastic modeling strategy in order to take into account the presence of uncertainties. However, the stochastic finite element modeling of a more complex engineering structure composed by a large number of degrees of freedom, or its use in dynamic analyses requiring several evaluations such as in optimization and model updating, the computational cost can be prohibited or sometimes unfeasible. In these situations, the proposition of condensation strategy especially adapted for the resulting stochastic systems is interesting. This paper is devoted to the investigation of a robust model condensation strategy to reduce the random matrices of the stochastic system. The basis to be used is formed by a nominal basis evaluated by performing firstly an eigenvalue problem of the mean model enriched by static residues due to the small modifications introduced. To illustrate the main features and capabilities of the proposed strategy, numerical simulations were performed for a plate model in which the stochastic mass and stiffness matrices were generated by applying the so-called Karhunen-Loève expansion. The stochastic results are presented in terms frequency response function envelopes for the full and reduced stochastic dynamic systems subjected to a deterministic excitation.