Conditions under which the time response of certain distributed parameter systems, which are assumed to possess “classical normal” modes, is critically damped, overdamped, or underdamped are presented. The conditions are derived from the definiteness of certain combinations of the coefficient operators of the describing equations. These conditions are compared to previous results and their usefulness is illustrated by examples.
The Nature of the Temporal Solutions of Damped Distributed Systems With Classical Normal Modes
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Inman, D. J., and Andry, A. N., Jr. (December 1, 1982). "The Nature of the Temporal Solutions of Damped Distributed Systems With Classical Normal Modes." ASME. J. Appl. Mech. December 1982; 49(4): 867–870. https://doi.org/10.1115/1.3162629
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