20 40 60 80 100 120 140 0 200 400 600 800 1000 1200 1400 1600 Bell Eigenvalues. 16 D.o.f. k 2-3 [%] Freq. [Hz] 20 40 60 80 100 120 140 0 200 400 600 800 1000 1200 1400 1600 Bell Eigenvalues. 16 D.o.f. k 2-3 [%] Freq. [Hz] Figure 7 – Natural frequencies of the structure versus angle configuration . At the end of this paragraph it is possible to assert that curve crossing and curve veering are phenomena tightly linked with physical parameters and their occurrence depends on symmetric or nonsymmetric properties. In particular, a slight loss of symmetry allows to obtain curve veering in a system with only curve crossing phenomena. Also in these last systems, crossing phenomena may be again present, if different eigenspaces with independent eigenvalues are interacting. The properties of symmetry is not, therefore, a fundamental requirement to have a system with coincident or very closed modes. Finally, MAC is an efficient tool to discriminate crossing and veering phenomena. TEST RIG DESCRIPTION Main ideas of the test bench are to obtain a structure without symmetric and cyclic properties but with dynamics behaviour characterised by coincident eigenvalues (curve crossing) and/or close eigenvalues (curve veering). Observing the dynamic instability of flutter phenomena, the structure shown in Figure 8 has a very simplified wing shape, where a sensitive geometrical parameter is chosen to change its dynamic properties. Figure 8 – Sketch of the test rig. C C C C C C C V V V V C 331
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