Criticality of Damping in Multi-Degree-of-Freedom Systems

[+] Author and Article Information
A. Bhaskar

Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, UK

J. Appl. Mech 64(2), 387-393 (Jun 01, 1997) (7 pages) doi:10.1115/1.2787320 History: Received November 19, 1992; Revised April 06, 1994; Online October 25, 2007


The concept of criticality in multi-degree-of-freedom systems is discussed. Sufficient conditions for overdamping, critical damping, and underdamping are derived in terms of the matrices appearing in the modal coordinates. It is noted that results available in the literature for the case of overdamping and mixed damping are erroneous. This has been pointed out by Bhaskar (1991, 1992) for the cases of overdamping and mixed damping, and by Barkwell et al. (1992) for the case of overdamping. The error in the proof of the conditions for overdamping is brought out. A sufficient condition for overdamping is presented. Results obtained for the symmetric systems are then generalized to the symmetrizable systems. Theorems on eigenvalue bounds are applied to establish criticality.

Copyright © 1997 by The American Society of Mechanical Engineers
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