PREPRINT MASSA F., LEROUX A., LALLEMAND B., TISON T., MARY S., BUFFE F. (2011). Fuzzy vibration analysis and optimization of engineering structures Appli- cation to Demeter satellite. IUTAM bookseries, 27(1), pp. 63-76, ISSN 978-94- 007-0289-9_5 Contact: franck.massa@univ-valenciennes.fr Fuzzy vibration analysis and optimization of engineering structures Application to Demeter satellite F. Massa 1 , A. Leroux 1 , B. Lallemand 1 , T. Tison 1 , F. Buffe 2 , S. Mary 2 1 Laboratoire d'Automatique, de Mécanique et d’Informatique industrielles et Humaines - LAMIH UMR CNRS 8530 - Université de Valenciennes et du Hainaut Cambrésis - Le Mont Houy - 59313 Valenciennes Cedex 9 – France - Tel: +33 (0)3.27.51.14.59 2 Centre National d’Etudes Spatiales - 18 Avenue Edouard Belin - 31401 Toulouse Cedex 9 Abstract The objective of this paper is to highlight that the fuzzy approaches can be employed in a design phase in order to build a robust engineering structure. An optimization problem, in which design variables, constraints and objectives func- tions are considered as fuzzy, is defined. To determine the optimized feasible de- sign space, a specific methodology, based on genetic algorithms, is proposed. 1 Introduction Although the deterministic numerical simulations are more and more efficient, many sources of uncertainties can always affect structures behaviour prediction. Uncertainties are principally due to a lack of knowledge of the endogenous or ex- ogenous parameters. Different approaches have then been developed to take these imperfections into account. Amongst these ones, the fuzzy subsets theory [1] al- lows to model both imprecise data and subjective data. This formalism has already been employed successfully by several researchers to study different problems [2- 4], such as static, modal or dynamic, defined with uncertainties. In this paper, a non-deterministic approach is performed in an optimization process in order to improve an existing design of a structure by integrating the identified uncertainties. This study relies on an efficient propagation method to calculate fuzzy frequencies, which are used as constraints functions in the optimi- zation problem, and on the use of genetic algorithms to explore the design space.