Output details

On veering of eigenvalue loci

Significance of output:

Eigenvalue veering, or avoided-crossing, occurs widely in engineering and physics. Typically, the eigenvalues (possibly natural frequencies squared) are plotted as some parameter of the system is varied. The phenomenon is associated with localisation, which can lead to high amplitudes of vibration, and possible fatigue failures. Existing approaches to characterise veering include eigenvalue and eigenvector derivatives. This paper presents a simple new paradigm to characterise the phenomenon, in terms of a centre of veering and the geometry of a standard north-south hyperbola. The latter is achieved through a coordinate translation and rotation.