Almost Classically Damped Continuous Linear Systems

[+] Author and Article Information
S. Natsiavas

Department of Mechanical Engineering, Aristotle University of Thessalonki, 54006 Thessaloniki, Greece

J. L. Beck

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125

J. Appl. Mech 65(4), 1022-1031 (Dec 01, 1998) (10 pages) doi:10.1115/1.2791896 History: Received July 22, 1997; Revised April 03, 1998; Online October 25, 2007


The dynamic response of a general class of continuous linear vibrating systems is analyzed which possess damping properties close to those resulting in classical (uncoupled) normal modes. First, conditions are given for the existence of classical modes of vibration in a continuous linear system, with special attention being paid to the boundary conditions. Regular perturbation expansions in terms of undamped modeshapes are then utilized for analyzing the eigenproblem as well as the vibration response of almost classically damped systems. The analysis is based on a proper splitting of the damping operators in both the field equations and the boundary conditions. The main advantage of this approach is that it allows application of standard modal analysis methodologies so that the problem is reduced to that of finding the frequencies and mode shapes of the corresponding undamped system. The approach is illustrated by two simple examples involving rod and beam vibrations.

Copyright © 1998 by The American Society of Mechanical Engineers
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