0 5 10 15 20 25 30 10−8 10−7 10−6 10−5 10−4 10−3 10−2 mode number Δωj Fig. 2 Truss frame: relative frequency error Δωj =' ' ' ωfull j −ωDCB j ' ' ' ωfull j for the Dual Craig-Bampton with (red triangles) and without interface reduction (blue squares). In order for the first 30 eigenfrequencies to have a relative error of maximum 1% (as in the previous example), one requires 10 vibration modes per substructures (this is determined by trial and error when no interface reduction is applied). We then look for the number of interface modes needed to maintain an maximum relative error of 1%. This is achieved with 62 interface modes. The results are depicted in figure 4. For this case we note that the interface reduction significantly decreases the dimension of the reduced problem. Indeed, since there are 252 interface compatibility constraints1 the effective dimension of the reduced problem is 360 without interface reduction, and 128 after interface reduction. Note that with 128 generalized degrees of freedom w are able to approximate accurately 30 modes, which shows the efficiency of the Dual Craig-Bampton with interface reduction. 1 In our implementation we use 276 Lagrange multipliers since all redundant compatibility conditions are consider for simplicity at corners. Interface Reduction in the Dual Craig-Bampton method 323
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