Technical Briefs

On Veering of Eigenvalue Loci

[+] Author and Article Information
N. G. Stephen

Mechanical Engineering, School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UKngs@soton.ac.uk

J. Vib. Acoust 131(5), 054501 (Sep 10, 2009) (5 pages) doi:10.1115/1.3147130 History: Received September 26, 2008; Revised April 29, 2009; Published September 10, 2009

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 equation 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.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Two degree-of-freedom spring-mass system and its graph, denoted P2

Grahic Jump Location
Figure 2

The graph of a chain of n coupled oscillators, denoted Pn

Grahic Jump Location
Figure 3

Eigenvalue loci for system in Fig. 1, with m1=m2=k2=1 and varying k1; the coupling spring has stiffness s=0.05. Also shown is the center of veering, and anticlockwise coordinate rotation.

Grahic Jump Location
Figure 4

Eigenvalue loci for system in Fig. 1, with m2=k1=k2=1 and varying m1; the coupling spring has stiffness s=0.05




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In