Optimization of the Dynamic Behaviour of Complex Structures Based on a Multimodal Strategy

Abstract

The use of a modal approach to describe a structure from the standpoint of optimizing its dynamic behavior offers multiple advantages. Once modal matrices have been computed, optimization criteria can be readily defined. Both the dynamic amplification phenomena and dynamic coupling between substructures can then be described using just a small number of degrees of freedom. Furthermore, it becomes possible to link the criteria to the modal parameters used in the systemic procedure. In this chapter, we will propose optimization criteria based on a multimodal description of complex structures. The modal synthesis technique presented herein is based on the double and triple-modal synthesis proposed by Besset & Jezequel (2008a;d), as well as on classical component mode synthesis methods like those developed by Craig & Bampton (1968) or Hurty (1965). According to these modal synthesis techniques, many boundary degrees of freedom are capable of remaining; in such cases, numerical costs will also remain high. In order to avoid a high-cost situation, we are proposing generalized modal synthesis methods that operate by introducing generalized boundary coordinates in order to describe substructure connections: this procedure is called a “double modal synthesis”. In addition, we are proposing another procedure to analyze structures coupled with fluid. This second procedure will then be called “triple modal synthesis”. The first modal synthesis is classical; it consists of representing the interior points of the fluid by acoustic modes. When considering a formulation in force, the pressure on boundary points is set equal to zero. Using a formulation in displacement, cavity modes are introduced, generating a correspondence to the free modes of a structure. The second modal synthesis consists of describing the boundary forces between the fluid and each substructure through use of a set of loadedmodes. Lastly, the third modal synthesis consists of describing the boundary forces between each substructure by introducing another set of loaded modes. Complex structures often include hollow parts and stiffeners, both of which require very accurate analysis in order to obtain satisfactory results. In this chapter, the term “hollow parts” will denote the formed steel and stiffeners that make up the skeleton of a structure. In complex structures such as automobiles, stiffeners and formed steel parts, which compose the skeleton of the structure, these parts are most responsible for overall structural behavior. To analyze these elements, the method used is the one proposed in Besset & Jezequel (2008b). 5