36 Reduced-Order Modelling for Investigating Nonlinear FEM Systems 345 15 20 25 30 35 40 45 Frequency (Hz) 0 0.05 0.1 0.15 0.2 0.25 U1 NNM1 N=1 NNM2 N=1 NNM1 N=13 NNM2 N=13 NNM1 N=25 NNM2 N=25 NNM1 N=37 NNM2 N=37 NNM1 N=49 NNM2 N=49 NNM1 N=52 NNM2 N=52 Fig. 36.7 Nonlinear normal modes projected in the first mode obtained retaining the first two modes adopting the AMF for a set of symmetric configuration. The set of masses start at Nposition – defined in the legend – counted starting from the main beam 15 20 25 30 35 40 45 Frequency (Hz) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 U2 NNM1 N=1 NNM2 N=1 NNM1 N=13 NNM2 N=13 NNM1 N=25 NNM2 N=25 NNM1 N=37 NNM2 N=37 NNM1 N=49 NNM2 N=49 NNM1 N=52 NNM2 N=52 Fig. 36.8 Nonlinear Normal Modes projected in the first mode obtained retaining the first two modes adopting the AMF for a set of symmetric configuration. The set of masses start at Nposition – defined in the legend – counted starting from the main beam done for the second NNM, the amplitude (frequency) is apparently increasing (decreasing) until the position 49 is reached. At such a position a sudden decrease in amplitude occurs and after such a position, the amplitude and frequency do not change significantly. The stated inversion of behaviour is linked to the change of modal shape of the normal mode. The first (second) mode presents a switch of modal behaviour; from being predominantly flexional (torsional) becomes predominantly torsional (flexional). 36.4.2 Case b As for the symmetric case, the first two modes have been considered and effects of the asymmetric stated parametric variation on linear and nonlinear behaviour have been investigated looking at nonlinear normal modes. The set of masses is varied asymmetrically changing the position of the masses just on one side of the crossed beam. Figures 36.9 and 36.10 shows the
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