Structured pseudospectra and random eigenvalues problems in vibrating systems

Wagenknecht, T., Green, K., Adhikari, S. and Michiels, W. (2006) Structured pseudospectra and random eigenvalues problems in vibrating systems. AIAA Journal, 44(10), pp. 2404-2414. (doi: 10.2514/1.21486)

Abstract

This paper introduces the concept of pseudospectra as a generalized tool for uncertainty quantification and propagation in structural dynamics. Different types of pseudospectra of matrices and matrix polynomials are explained. Particular emphasis is given to structured pseudospectra for matrix polynomials, which offer a deterministic way of dealing with uncertainties for structural dynamic systems. The pseudospectra analysis is compared with the results from Monte Carlo simulations of uncertain discrete systems. Two illustrative example problems, one with probabilistic uncertainty with various types of statistical distributions and the other with interval type of uncertainty, are studied in detail. Excellent agreement is found between the pseudospectra results and Monte Carlo simulation results.

• Item Type: Articles
• Additional Information: T. W.’s and K. G.’s research was supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant No. GR/ 535684/01. S. A. acknowledges the support of the EPSRC through the award of an advanced research fellowship, Grant No. GR/ T03369/01. W. M.’s research is sponsored by the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Adhikari, Professor Sondipon
• Authors: Wagenknecht, T., Green, K., Adhikari, S., and Michiels, W.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: AIAA Journal
• Publisher: American Institute of Aeronautics and Astronautics, Inc.
• ISSN: 0001-1452
• ISSN (Online): 1533-385X
• Published Online: 01 January 1970