A ROBUST CONDENSATION STRATEGY FOR STOCHASTIC DYNAMIC SYSTEMS
DOI:
https://doi.org/10.26512/ripe.v2i16.21619Keywords:
Parametric uncertainties. Robust condensation. Stochastic finite elements method. Dynamics.Abstract
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.
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References
Craig, Jr. R. R. and Kurdila, A. J., 2006. Fundamentals of Stuctural Dynamics. John Wiley & Sons, New-Jersey.
de Lima, A. M G., Rade, D. A. and Bouhaddi, N., 2010a. Stochastic modeling of surface viscoelastic treatments combined with model condensation procedures. Shock and Vibration, Vol. 17, p. 429-444.
de Lima, A.M.G.; da Silva, A.R.; Rade, D.A.; Bouhaddi, N., 2010b. Component mode synthesis combining robust enriched Ritz approach for viscoelastically damped structures. Engineering Structures, vol. 32, pp. 1479-1488.
Florian, A., 1992. An efficient sampling scheme: updates Latin Hypercube sampling. Probabilistic Engineering Mechanics, vol. 7(2), pp. 123-130.
Gèrges, Y., 2013. Méthodes de reduction de modèles en vibroacoustique non-linéaire. PhD Thesis, Université de Franche-Comté, Besançon.
Ghanem, R. G. and Spanos P. D., 1991. Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, New York.
Masson G, Ait Brik B, Cogan S, Bouhaddi N., 2006. Component mode synthesis (CMS) based on an enriched Ritz approach for efficient structural optimization. J Sound Vib, vol. 296, pp. 845-860.
Ribeiro, L. P., 2015. Modelagem Estocástica de Estruturas Compósitas Incorporando Circuitos Shunt para o Controle Passivo de Vibrações. MSc Dissertation, Universidade Federal de Uberlândia, Uberlândia.
Ritto, T. G.; Sampaio, R.; Cataldo, E., 2008. Timoshenko beam with uncertainty on the boundary conditions, Journal of ABCM, vol. 30 (4), p. 295-303.
Rosa, U.L. and de Lima, A.M.G., 2016. Fatigue analysis of stochastic systems subjected to cyclic loading in the frequency domain, In Proceedings of the 3rd International Symposium on Uncertainty Qualification and Stochastic Modeling.
Rubinstein, R. Y., 1981. Simulation and the Monte Carlo Method. John Wiley & Sons, New Jersey.
Schueller, G. I., 2001. Computational stochastic mechanics - recent advances. Journal of Computers and Structures, vol. 79, p. 2225-2234.
Soize, C., 2000. A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, Elsevier, vol. 15 (3), p. 277-294.
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