Snap-through under unilateral displacement control with constant velocity

Abstract

When the side of a beverage can or the domed lid of a jar is pushed inward, all or part of the structure may suddenly snap into an inverted configuration. The velocity of the pushing motion affects this instability. Most previous analyses of snap-through have considered force control (increasing the pushing force, e.g., a weight). Snap-through under dynamic, unilateral displacement control is investigated here, with the indentor moving at constant velocity (as in a universal testing machine) until snap-through occurs. Shallow elastic arches with immovable pinned ends are analyzed. Attention is focused on the critical height of the indentor at which snap-through is initiated. The effects of the indentor velocity, indentor location along the span, initial arch height, and damping magnitude are investigated. In addition, experiments are conducted on shallow buckled beams, which behave similarly to arches. Usually, the higher the indentor velocity, the further the indentor must move before snap-through occurs.