Dynamic snapping of a suddenly loaded elastica with fixed end slopes

Abstract

In this paper we study the dynamic snapping of an elastica with fixed end slopes. Both ends of the elastica are clamped, with one fixed in space and the other allowed to slide along a linear track. An edge thrust is applied suddenly on the sliding clamp, causing the elastica to undergo a snap-through jump. This setup can be used as a bistable device. The interest of this paper is to determine the critical value of the suddenly applied edge thrust causing snap-through, termed dynamic snapping load. With use of deformation potentials, the equations of motion of the elastica-slider assembly are rearranged, taking into account the effects of both the slider mass and damping. Finite difference method is adopted to discretize the resulted equations. In order to ensure the convergence of the numerical scheme, a linearization approach has to be adopted when the slider mass is non-zero. It is observed that for the setup studied in this paper, the dynamic snapping load is about 90% of its static counterpart. The viscous damping associated with the end slider in general has a favorable tendency of raising the dynamic snapping load. Somewhat unexpectedly, although the slider mass affects the transient response of the elastica-slider assembly significantly, it has no effect on the dynamic snapping load.