CONCLUSIONS The paper presents a theoretical analysis and an experimental test rig on a nonsymmetric structure with eigenvalues curve veering and crossing phenomena. Detailed numerical models on lumped parameters systems and continuous systems with coincident and/or close eigenvalues are examined to developed a numerical FE model suitable to describe the tunable and simple test rig with coincident eigenvalues and curve veering phenomena without symmetric properties or completely uncoupled dynamic systems. A consistent numerical FE model has been developed to design the structure. The initial comparison between the experimental data obtained through the test rig and the numerical results seems to be suitable for validate the methodology. The test bench is useful to investigate curve veering phenomena with an experimental overview. It allows to completely control the dynamic behaviour through a physical system parameters, and it could also be a consistent tool, due to its form similar to a wing, to understand flutter dynamic instability through coupling bending wing mode with torsional one. BIBLIOGRAPHY [1] Leissa W., “On a curve veering aberration”, Journal of Applied Mathematics and Physics (ZAMP), 25, 1974, pp. 99-111. [2] Kutter J.R., Sigillito V.G., “On curve veering”, Journal of Sound and Vibration, 75, 1981, pp. 585-588. [3] Perkins N.C., Mote C.D.Jr., “Comments on curve veering in eigenvalue problems”, Journal of Sound and Vibration, 106(3), 1986, pp. 451-463. [4] Pierre C., “Mode localization and eigenvalue loci veering phenomena in disordered structures”, Journal of Sound and Vibration, 126(3), 1988, pp. 485-502. [5] Chen X., Kareem A., “Curve Veering of Eigenvalue Loci of Bridges with Aeroelastic Effects”, Journal of Engineering Mechanics, 129(2), 2003, pp. 146-159. [6] Yoo H.H., Shin S.H., “Vibration analysis of rotating cantilever beams”, Journal of Sound and Vibration, 212(5), 1998, pp. 807-828. [7] Balmès E., “High modal density, curve veering, localization: a different perspective on the structural response”, Journal of Sound and Vibration, 161(2), 1993, pp. 358-363. [8] Mugan A., “Effect of mode localization on INPUT-OUTPUT directional properties of structures”, Journal of Sound and Vibration, 258(1), 2002, pp. 45-63. [9] Liu X.L., “Behaviour of derivatives of eigenvalues and eigenvectors in curve veering and mode localization and their relation to close eigenvalues”, Journal of Sound and Vibration, 256(3), 2002, pp. 551-564. [10] Adhikari S., “Rates of change of eigenvalues and eigenvectors in damped dynamic system”, AIAA Journal, 39(11), 1999, pp. 1452-1457. [11] Young L.J., Hwang M. C., "Curve Veering Phenomena One-Dimensional Eigenvalue Problems", Proceedings of the Eighteenth National Conference of the Chinese Society of Mechanical Engineers, 12, 2001, Taipei, Taiwan, R.O.C., pp. 239-246. [12] Du Bois J.L., Adhikari S., Lieven N.A.J., “Eigenvalue curve veering in stressed structures: An experimental study”, Journal of Sound and Vibration, 322, 2009, pp. 1117-1124. 336
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