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TECHNICAL PAPERS

Veering Phenomena in Systems With Gyroscopic Coupling

[+] Author and Article Information
Stefano Vidoli

Dipartimento di Ingegneria Strutturale e Geotechnica, Università degli Studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italiastefano.vidoli@uniromal.it

Fabrizio Vestroni

Dipartimento di Ingegneria Strutturale e Geotechnica, Università degli Studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italiavestroni@uniromal.it

J. Appl. Mech 72(5), 641-647 (Feb 14, 2004) (7 pages) doi:10.1115/1.1940666 History: Received June 20, 2003; Revised February 14, 2004

The sharp divergence of two root-loci for a critical value of the parameters is called veering. Veering phenomena are interesting since they involve relevant energetic exchanges between the eigenmodes and strongly affect the undamped forced response of the system. A straightforward perturbation approach has already been used in the literature to analyze the dependence of the eigensprectrum on a system parameter and formulate a veering criterion. This perturbation approach and other ideas are generalized to the study of veering in discrete and continuous systems with gyroscopic operators of internal coupling and the results applied to a real electromechanical interaction.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 5

The eigenvalues for h=1, 5 in the clamped case of boundary conditions. Darker regions indicate veering phenomena.

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Figure 4

Assembled plate and electric network

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Figure 3

Frequency-response function H21(Ω) for different values of the ratio B∕A (black B∕A=11; gray B∕A=1.25; dashed B∕A=0.75)

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Figure 2

Veering and crossing geometry: (a) eigenvalues as functions of B; (b) eigenvectors components as functions of B

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Figure 1

Sequences of ellipses starting and ending in the same points of E. The major axes are depicted as thin gray lines.

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