The Effect of Spatial Distribution on Dynamic Snap-Through

Abstract

The effect of the spatial distribution of impulsive loads on dynamic snap-through of a shallow circular arch is considered in detail. The Budiansky-Roth criterion is used to establish critical magnitudes of the load for many distributions by numerical integration of an approximate set of equations obtained by Galerkin’s method. It is necessary to distinguish between snap-through on the initial oscillation (immediate) and snap-through occurring during a finite time of the response. Critical magnitudes for both cases are compared to a distribution independent lower bound obtained from an analysis of the critical points. For all distributions considered the lower bound is a less conservative estimate of the critical magnitude for finite time snap-through than for immediate snap-through. The effect of small damping on this conclusion, however, remains an open question.