318 O. Giannini et al. 115 110 105 100 frequency(Hz) frequency(Hz) frequency(Hz) 95 90 85 0.05 0 0.1 damping(%) Locus Plot c b a Locus Plot 92.4 92.35 92.3 92.25 92.2 2 4 6 damping(%) 8 x 10-3 0.15 0.2 115 Mode 1 of Beam 1, from Beam 1 exc. - Beam 1 resp. Mode 2 of Beam 2, from Beam 2 exc. - Beam 2 resp. 110 105 100 95 90 85 0 10 20 mass(g) 30 40 Fig. 29.12 Experimental evaluation of the crossing in asymmetrically damped systems: (a) locus plot, (b) veering plot, (c) zoom of locus plot around beam2 mode Disk Tip Beam Elecric Motor Disk shaft Speed reducer Belt and pulleys Disk Beam Thin plates α Beam Support a b Fig. 29.13 Beam on disc setup (a) picture of the set-up; (b) schematic 29.5 Conclusions In coupled systems, two eigenvalues interact when they are “close” to each other. Three main types of interactions can occur: veering, lock-in or crossing and consequently system response is generally largely affected by the type of interaction. Among the different results shown in this paper, it is worthwhile to point out that the damping, when not uniformly distributed among the degrees of freedom of the system, affects the eigenvalue interaction in a radical way. In particular, contrary to the general feeling, while a high damping merges two close peaks in the FRF, it may induce a transition from veering to crossing, allowing the two modes to keep their individuality. This is reflected in the coupled FRF where the presence of two modes at the same frequency produce, because of their phase difference, and antiresonance with the peak of the other mode.
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