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TECHNICAL PAPERS

Left Eigenvectors: Extraction From Measurements and Physical Interpretation

[+] Author and Article Information
I. Bucher, S. G. Braun

Technion-lsrael Institute of Technology, Technion City, Haifa 32000, Israel

J. Appl. Mech 64(1), 97-105 (Mar 01, 1997) (9 pages) doi:10.1115/1.2787300 History: Received February 25, 1995; Revised February 02, 1996; Online October 25, 2007

Abstract

In this paper the extraction of left eigenvectors from measured frequency response functions is presented and discussed. It is shown that contrary to the extraction of right eigenvectors from measured response data, the extraction of left eigenvectors is inherently ill-posed when the same measured information is being used. The ill-posedness can result in a spatially oscillating additive component (short wavelength) appearing in the identified left eigenvectors, a property which is not described in existing literature on structural dynamics. Some well-known regularization methods are hence used to reduce the inaccuracies appearing in the extracted left eigenvectors. It is also shown that a further improvement in the accuracy of the solution can be achieved by making use of an approximation of the mass distribution combined with regularization. Throughout this paper, an attempt is made to provide a physical insight to the various aspects related to the left eigenvectors and their extraction. This includes (a) the interpretation of left eigenvectors as internal force distributions; (b) the inherent reason for the ill-conditioning, and (c) the spatial filtering of short wavelength achieved by regularization, yielding an improved estimate of the left eigenvectors.

Copyright © 1997 by The American Society of Mechanical Engineers
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