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Almost Classically Damped Continuous Linear Systems

Natsiavas, S. and Beck, J. L. (1998) Almost Classically Damped Continuous Linear Systems. Journal of Applied Mechanics, 65 (4). pp. 1022-1031. ISSN 0021-8936. doi:10.1115/1.2791896.

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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.

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Additional Information:© 1998 The American Society of Mechanical Engineers. Received July 22, 1997; revised Apr. 3, 1998.
Subject Keywords:Linear systems, Vibration, Boundary-value problems, Damping, Shapes, Dynamic response, Equations
Issue or Number:4
Record Number:CaltechAUTHORS:20120829-144806892
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Official Citation:Natsiavas SS, Beck JL. Almost Classically Damped Continuous Linear Systems. ASME. J. Appl. Mech. 1998;65(4):1022-1031. doi:10.1115/1.2791896
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33683
Deposited By: Carmen Nemer-Sirois
Deposited On:05 Sep 2012 22:11
Last Modified:09 Nov 2021 21:36

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