Forced Vibration of a Damped Combined Linear System

[+] Author and Article Information
L. A. Bergman

Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. W. Nicholson

Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Vib., Acoust., Stress, and Reliab 107(3), 275-281 (Jul 01, 1985) (7 pages) doi:10.1115/1.3269257 History: Received May 13, 1985; Online November 23, 2009


A new and general method for determining the exact undamped natural frequencies and natural modes of vibration, the orthogonality relation for the natural modes, and the response to arbitrary excitation for both damped and undamped combined linear systems is given. The method, based upon Green’s functions of the vibrating distributed subsystems, is demonstrated for a multiplicity of linear oscillators connected to a simple beam.

Copyright © 1985 by ASME
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