On veering of eigenvalue loci
On veering of eigenvalue loci
Eigenvalue veering is studied in the context of two simple oscillators coupled by a (presumed weak) spring, variants of which have been considered by several authors. The concept of a center of veering is introduced, leading to a coordinate translation; a subsequent coordinate rotation, dependent on the degree of asymmetry of the system, reduces the frequency equaiton to a standard north-south opening hyperbola. Thus veering occurs even when coupling is strong, and may be characterized by these coordinate transformations and geometric features of the hyperbola, rather than eigenvalue and eigenvector derivatives.
eigenvalue, loci, eigencurve, veering
054501-[5pp]
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
October 2009
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Stephen, N.G.
(2009)
On veering of eigenvalue loci.
Journal of Vibration and Acoustics, 131 (5), .
(doi:10.1115/1.3147130).
Abstract
Eigenvalue veering is studied in the context of two simple oscillators coupled by a (presumed weak) spring, variants of which have been considered by several authors. The concept of a center of veering is introduced, leading to a coordinate translation; a subsequent coordinate rotation, dependent on the degree of asymmetry of the system, reduces the frequency equaiton to a standard north-south opening hyperbola. Thus veering occurs even when coupling is strong, and may be characterized by these coordinate transformations and geometric features of the hyperbola, rather than eigenvalue and eigenvector derivatives.
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Published date: October 2009
Keywords:
eigenvalue, loci, eigencurve, veering
Organisations:
Computational Engineering and Design
Identifiers
Local EPrints ID: 69730
URI: http://eprints.soton.ac.uk/id/eprint/69730
ISSN: 1048-9002
PURE UUID: 1f5be5c0-78c3-4fe8-bd77-5bebac1c459e
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Date deposited: 30 Nov 2009
Last modified: 13 Mar 2024 19:43
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