Selection of the nature of the unknown of the problem is thus important for the resulting matrix structure. For vibro-acoustics, this is the case when the problem is written in pressure perturbations for the fluid and displacements for the structure. In this study, the classical displacement-pressure formulation is used. Some of the bottlenecks of these kinds of computations are the excessive computation times and the computer resources used for storage. Model order reduction techniques are well established in the structural field, such as the Craig-Bampton fixed interface [5] and Rubin free interface methods [6]. In the context of this research paper, we are concerned with the extension of the standard Craig-Bampton reduction method to the modelling of vibro-acoustic simulation of systems that are strongly coupled. Approximations of global representations are added to the basis representation to enrich the Craig-Bampton reduction space. These approximation vectors result from a new iterative solver, iterative reduced correction algorithm, that is still under development/improvement. In the context of the paper, a short theory overview and the common matrix equations are going to be provided in section 2.1. Section 2.2 will outline the symmetrization concept that is at the heart of the iterative algorithm. Section 2.3 will summarize the iterative correction algorithm. Section 3 will show the extension of the method to substructuring through the use of classical CraigBampton scheme. Section 4 will summarize the developed computational framework and includes a numerical example with results. In the last section, some discussions are provided. 2 Theoretical backgound and outline 2.1 Governing equations of the problem For a formulation in terms of displacement uand nodal pressure perturbation p, the discretization of the governing differential equations for vibro-acoustics and of the coupling conditions on the interacting interfaces, results in (e.g. [4]) Ms 0 Mfs Mf ¨u ¨p + Ks Ksf 0 Kf u p = Fs Ff . (1) Fluids interacting with their surrounding structure couple through the continuity of the velocity on the interface and the equilibrium of the interface stresses/pressures, which results in the off-diagonal coupling blocks. A closed form relation exists between the off-diagonal coupling blocks, namely, Mfs =−ρKT sf . With the use of this relation, one might write Ms 0 −KT sf Mf ρ ¨u ¨p + Ks Ksf 0 Kf ρ u p = Fs Ff ρ . (2) Umut Tabak and Daniel J. Rixen 264
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