A Truly Hybrid Approach to Substructuring Problems Using Mixed Assemblyand Implicit Solving Strategies S.N. Voormeeren, P.L.C. van der Valk and D.J. Rixen Abstract In recent years, the structural dynamic community showed a renewed interest in component coupling (i.e. dynamic substructuring) and decoupling techniques for structural dynamic analysis of assembled systems. Especially for hybrid problems, where some component models are obtained fromexperimental data and others fromnumerical modeling, these techniques offer interesting possibilities. However, since measured models are generally expressed in terms of flexibility and numerical models in terms of stiffness, model inversions are needed at least at the component interfaces. This leads to increased computational effort and/or amplification of measurement errors. To avoid the inversions of the component models, a truly hybrid approach to coupling and decoupling problems is proposed in this paper. Using a mixed assemblymethodology derived froma so-called “three field formulation”, stiffness type components can be directly assembled to flexibility based subsystems. Then only the interface problemremains to be solved. In part one of this paper the theoretical derivation of the proposedmethodology is addressed. Furthermore, we outline the differences with respect to the existingmethods. 1 Introduction 1.1 Dynamic Substructuring Dynamic substructuring (DS) techniques have been well established over the past decades. These techniques consist in constructing the structural dynamic model of a large and complex systembyassembling the dynamic models of its simpler components (also called subsystems or substructures). In recent years, the structural dynamiccommunity showed a renewed interest in these substructure coupling techniques, especially in the context of experimental applications. Since the application of the DS methodology using experimental models is usually performed in the frequency domain, using component frequency response function (FRF) matrices, these techniques are often termedfrequency based substructuring (FBS). In FBS, two classes of problems can be distinguished. In the first class the coupling problemis considered, where the also referred to as the “forward” problem. The second class of problems considers the reverse case, namely how a substructure model can be found fromtheassembledsystem. This decouplingproblemis sometimes also referred to as “backward” analysis. In this paper we will focus only on the coupling problemindynamic substructuring. Anexperimental FBS analysis consists in finding the structural dynamic behavior of a systemcomposedof multiple components, where at least one component model is derived experimentally. This is sometimes also called “hybrid” analysis. Although the basic theory of dynamic substructuring has been formulated decades ago, successful application of experimental FBS techniques is often limited to relatively simple systems. Application to complex real-life engineering structures is often hindered by the method’s notorious sensitivity to experimental errors. Corresponding author: Sven Voormeeren Delft University of Technology, Mekelweg 2, 2628CD Delft, the Netherlands e-mail: s.n.voormeeren@tudelft.nl T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, DOI 10.1007/978-1-4419-9305-2_23, © The Society for Experimental Mechanics, Inc. 2011 dynamics of a systemare obtained by assembly of the dynamic models of its components. This couplingproblemis sometimes 329
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