taken as 1000kg/m3. The finite element model consists of 5250 quadrilateral structural and fluid elements, namely FLUID29 and PLANE42 elements in ANSYS. The total model consists of 6616 degrees of freedom. The model is partitioned into two similar components for the conducted numerical tests. The interface lines contain both the fluid and structural degrees of freedom. The test model is illustrated in Figure 2. The bold line represents the interface between the fluid and structure regions where the off-diagonal coupling blocks result from. The two ends of the beam are fixed for this problem. 1.5 m 0.29 m 0.06 m Fluid Domain Structural Domain Fig. 2 Model of a rectangular cavity coupled to a beam The discussed substructuring techniques in Sections 3.1, 3.2 and 3.3 are used to compute the reduced eigenfrequencies of the coupled system. We will start out the reduction studies with a modal basis where the structural variables, u, are expanded in the in-vacuo structural modes, u = φS ηS, and the fluid variables, p, are also expanded in the rigid walled acoustic cavity modes, p= φF ηF [20]. Resulting in, u p = φS 0 0 φF ηS ηF . (44) This diagonal reduction and projection basis is used in order to show the improvement with respect to this basis. During the numerical tests, 30 mode vectors are kept in the bases. One exception is the implementation of the scheme of Section 3.3 where some combination of fixed interface and global modes are used. 4.2 Results The results of the proposed schemes are presented in this subsection. All the presented results are based on a relative frequency error which is computed with respect to the frequencies that are found by ANSYS on the full coupled model. Figure 3 represents the relative frequency error results of the proposed scheme in Section 3.1. The improvement on error levels by the use of IRCA vectors after some iterations are also indicated in the same result. For the current setting, 2 iterations are enough for IRCA to satisfy the tolerance criteria of 0.01 given by equation (21). The error levels marked with represent the results obtained after 1 iteration of the Globally enriched substructuring techniques for vibro-acoustic simulation 275
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