Asymptotic Treatment of Non-Classically Damped Linear Systems

[+] Author and Article Information
W. Fang, J.-G. Tseng, J. A. Wickert

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA 15213 USA

Appl. Mech. Rev 48(11S), S111-S117 (Nov 01, 1995) doi:10.1115/1.3005058 History: Online April 29, 2009


The presence of non-classical dissipation in a general discrete dynamic system is investigated through a perturbation method for the eigenvalues and vectors. Results accurate to second-order are obtained, with corrections to the base solution being expressed in terms of readily-calculated quadratic forms. Exact solutions, and the derived asymptotic ones, are compared with the predictions of the so-called method of approximate decoupling, in which certain non-classical dissipative terms are omitted from calculations in the eigenvalue problem. The perturbation method is discussed through its application in several examples, indicating circumstances in which a non-classically damped system can be well-approximated by an “equivalent” classically damped one. Somewhat surprisingly, the addition of non-classical damping does not necessarily increase the stability of all vibration modes, and the perturbation method is shown to be useful in identifying those critical modes.

Copyright © 1995 by The American Society of Mechanical Engineers
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