Bounds on Motions of Some Lumped and Continuous Dynamic Systems

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.