Bounds on Motions of Some Lumped and Continuous Dynamic Systems

[+] Author and Article Information
R. H. Plaut, E. F. Infante

Division of Applied Mathematics, Brown University, Providence, R. I.

J. Appl. Mech 39(1), 251-256 (Mar 01, 1972) (6 pages) doi:10.1115/1.3422621 History: Received August 21, 1970; Online July 12, 2010


Lumped and continuous systems subjected to general dynamic loads or perturbations are considered. The motions of these systems are assumed to be described by ordinary or partial differential equations with time-varying forcing terms. Upper bounds on the motions are derived with a Liapunov type of approach. The results are applied to some structural dynamics problems. Displacement bounds are determined for elastic columns, plates, and arches, and sufficient conditions for stability of arches against dynamic “snap-through” are obtained.

Copyright © 1972 by ASME
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