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Research Papers

Rayleigh Quotient and Dissipative Systems

[+] Author and Article Information
A. Srikantha Phani1

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UKskpa2@eng.cam.ac.uk

S. Adhikari

Department of Aerospace Engineering, University of Bristol, Queens Building, University Walk, Bristol BS8 1TR, UKs.adhikari@bristol.ac.uk

1

Corresponding author. Assistant Professor, Department of Mechanical Engineering, The University of British Columbia, 2054–6250 Applied Science Lane, Vancouver, B.C., V6T 1Z4, Canada.

J. Appl. Mech 75(6), 061005 (Aug 15, 2008) (6 pages) doi:10.1115/1.2910898 History: Received September 20, 2006; Revised December 02, 2007; Published August 15, 2008

Rayleigh quotients in the context of linear, nonconservative vibrating systems with viscous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and nonviscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix.

Copyright © 2008 by American Society of Mechanical Engineers
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