Eigenvalue curve veering is a phenomenon that has found relevance and application in a variety of structural dynamic problems ranging from localization and stability studies to material property determination. Contemporary metrics for quantifying veering can be ambiguous and difficult to interpret. This manuscript derives three normalized indices in an effort to reconcile the deficit; two of these quantify the physical conditions which produce the behavior while the third provides a definitive measure of the overall intensity of the effect. Numerical examples are provided to illustrate the application of the methods, which are expected to form a basis for the development of advanced analytical tools.
Issue Section:
Research Papers
Keywords:
eigenvalues and eigenfunctions
1.
Claassen
, R. W.
, and Thorne
, C. J.
, 1962, “Vibrations of a Rectangular Cantilever Plate
,” J. Aerosp. Sci.
JASSA7 0095-9820, 29
(11
), pp. 1300–1305.2.
Webster
, J. J.
, 1968, “Free Vibrations of Rectangular Curved Panels
,” Int. J. Mech. Sci.
IMSCAW 0020-7403, 10
, pp. 571–582.3.
du Bois
, J. L.
, Adhikari
, S.
, and Lieven
, N. A. J.
, 2007, “Experimental and Numerical Investigation of Mode Veering in a Stressed Structure
,” Proceedings of the 25th International Modal Analysis Conference
, Vol. 25
, p. 233.4.
du Bois
, J. L.
, Adhikari
, S.
, and Lieven
, N. A. J.
, 2009, “Eigenvalue Curve Veering in Stressed Structures: An Experimental Study
,” J. Sound Vib.
JSVIAG 0022-460X, 322
, pp. 1117–1124.5.
McIntyre
, M. E.
, and Woodhouse
, J.
, 1988, “On Measuring the Elastic and Damping Constants of Orthotropic Sheet Materials
,” Acta Metall.
AMETAR 0001-6160, 36
(6
), pp. 1397–1416.6.
Hodges
, C. H.
, 1982, “Confinement of Vibration by Structural Irregularity
,” J. Sound Vib.
JSVIAG 0022-460X, 82
, pp. 411–424.7.
Hodges
, C. H.
, and Woodhouse
, J.
, 1983, “Vibration Isolation From Irregularity in a Nearly Periodic Structure: Theory and Measurements
,” J. Acoust. Soc. Am.
JASMAN 0001-4966, 74
(3
), pp. 894–905.8.
Pierre
, C.
, and Dowell
, E. H.
, 1987, “Localization of Vibrations by Structural Irregularity
,” J. Sound Vib.
JSVIAG 0022-460X, 114
(3
), pp. 549–564.9.
Pierre
, C.
, 1988, “Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures
,” J. Sound Vib.
JSVIAG 0022-460X, 126
(3
), pp. 485–502.10.
Afolabi
, D.
, and Mehmed
, O.
, 1994, “On Curve Veering and Flutter of Rotating Blades
,” ASME J. Eng. Gas Turbines Power
JETPEZ 0742-4795, 116
, pp. 702–708.11.
Balmès
, E.
, 1993, “High Modal Density, Curve Veering, Localization: A Different Perspective on the Structural Response
,” J. Sound Vib.
JSVIAG 0022-460X, 161
(2
), pp. 358–363.12.
Benedettini
, F.
, Zulli
, D.
, and Alaggio
, R.
, 2009, “Frequency-Veering and Mode Hybridization in Arch Bridges
,” Proceedings of the 27th International Modal Analysis Conference
.13.
Igusa
, T.
, 1993, “Critical Configurations of Systems Subjected to Wide-Band Input
,” J. Sound Vib.
JSVIAG 0022-460X, 168
(3
), pp. 525–541.14.
Adhikari
, S.
, and Friswell
, M. I.
, 2007, “Random Matrix Eigenvalue Problems in Structural Dynamics
,” Int. J. Numer. Methods Eng.
IJNMBH 0029-5981, 69
(3
), pp. 562–591.15.
Adhikari
, S.
, 2007, “Joint Statistics of Natural Frequencies of Stochastic Dynamic Systems
,” Comput. Mech.
CMMEEE 0178-7675, 40
(4
), pp. 739–752.16.
Perkins
, N. C.
, and Mote
, C. D.
, Jr., 1986, “Comments on Curve Veering in Eigenvalue Problems
,” J. Sound Vib.
JSVIAG 0022-460X, 106
(3
), pp. 451–463.17.
Triantafyllou
, M. S.
, and Triantafyllou
, G. S.
, 1991, “Frequency Coalescence and Mode Localisation Phenomena: A Geometric Theory
,” J. Sound Vib.
JSVIAG 0022-460X, 150
(3
), pp. 485–500.18.
Afolabi
, D.
, 1991, “Modal Interaction in Linear Dynamic Systems Near Degenerate Modes
,” NASA
Technical Memorandum Report No. 105315.19.
Seyranian
, A.
, and Mailybaev
, A.
, 2003, “Interaction of Eigenvalues in Multi-Parameter Problems
,” J. Sound Vib.
JSVIAG 0022-460X, 267
(5
), pp. 1047–1064.20.
Seyranian
, A. P.
, Kirillov
, O. N.
, and Mailybaev
, A. A.
, 2005, “Coupling of Eigenvalues of Complex Matrices at Diabolic and Exceptional Points
,” J. Phys. A
JPHAC5 0305-4470, 38
(8
), pp. 1723–1740.21.
Kirillov
, O.
, Mailybaev
, A.
, and Seyranian
, A.
, 2005, “Unfolding of Eigenvalue Surfaces Near a Diabolic Point
,” J. Phys. A
JPHAC5 0305-4470, 38
, pp. 5531–5546.22.
Seyranian
, A.
, Lund
, E.
, and Olhoff
, N.
, 1994, “Multiple Eigenvalues in Structural Optimization Problems
,” Struct. Multidiscip. Optim.
ZZZZZZ 1615-147X, 8
(4
), pp. 207–227.23.
Altintas
, G.
, 2009, “Effect of Mass Based Imperfections on Behavior of Linear Vibrating Plates Near Degenerate Modes
,” J. Vib. Control
JVCOFX 1077-5463, 15
(2
), pp. 219–231.24.
Liu
, X. L.
, 2002, “Behaviour of Derivatives of Eigenvalues and Eigenvectors in Curve Veering and Mode Localisation and Their Relation to Close Eigenvalues
,” J. Sound Vib.
JSVIAG 0022-460X, 256
(3
), pp. 551–564.25.
Fox
, R. L.
, and Kapoor
, M. P.
, 1968, “Rates of Change of Eigenvalues and Eigenvectors
,” AIAA J.
AIAJAH 0001-1452, 6
(12
), pp. 2426–2429.26.
Nelson
, R. B.
, 1976, “Simplified Calculation of Eigenvector Derivatives
,” AIAA J.
AIAJAH 0001-1452, 14
(9
), pp. 1201–1205.27.
Warburton
, G. B.
, 1976, The Dynamical Behaviour of Structures
, 2nd ed., Pergamon
, Oxford/New York
.28.
Nair
, P. S.
, and Durvasula
, S.
, 1973, “On Quasi-Degeneracies in Plate Vibration Problems
,” Int. J. Mech. Sci.
IMSCAW 0020-7403, 15
, pp. 975–986.Copyright © 2011
by American Society of Mechanical Engineers
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