The Effect of Damping on Dynamic Snap-Through

Abstract

Dynamic snap-through criteria are compared for an impulsively loaded shallow circular arch modeled as a Kelvin-Voigt material. The Budinasky-Roth criterion is used in conjunction with direct numerical integration of an approximate set of motion equations to obtain critical magnitudes of the load as a function of small viscous damping and the spatial distribution of the load. These critical magnitudes are compared to a lower bound estimate which is independent of the load distribution and damping. This lower bound is a stability-sufficiency condition formulated by Hsu. The presence of small damping significantly increases the critical magnitudes with respect to the undamped results for non-symmetric loading, and thus indicates the conservative nature of the lower bound.