0 5 10 15 20 25 30 10−7 10−6 10−5 10−4 10−3 10−2 10−1 mode number Δωj Fig. 4 Two-dimensional solid: relative frequency error Δωj = ' ' ' ωfull j −ωDCB j ' ' ' ωfull j for the Dual CraigBampton with (red triangles) and without interface reduction (blue squares). Figure 6 represents again mode 30, but with and without interface reduction (as explained in the previous section). One can clearly see that the interface reduction allows even some more incompatibility on the interface, but without significantly changing the associated frequency nor the MAC number. In figure 7 we show the first six modes obtained from the statically condensed interface problem (32), namely Tdual,stat Xα Xλ Clearly the first 3 modes resemble strongly the true modes of the system. Mode 4 however exhibits very large interface incompatibility and has a negative eigenvalue. This indicates that mode 4 is a mode of which the Lagrange multiplier part xλk plays an important role in provide compatibility and need therefore to be include in the reduction basis of the interface. Interface Reduction in the Dual Craig-Bampton method 325
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