Snap-Through Time of Arches Is Controlled by Slenderness and Imperfections

Snap through occurs in elastic structures when a stable equilibrium configuration becomes unstable, resulting in rapid motion towards a new and distinct stable state. While static analyses of snap through are well documented, the dynamics of snap through remain underexplored, particularly in structures with natural curvature. Using a combination of finite element simulations and multiple-scales analysis, we show that the snap-through dynamics of an arch under a central point load are controlled by its slenderness and imperfections embedded in the system. As the slenderness increases, the snap-through dynamics slow down, and the mode of snap through changes from limit-point buckling to bifurcation buckling. When bifurcation buckling occurs, snap through is preceded by an extended period of oscillatory behavior. The duration of these pre-snap-through oscillations, and hence the snap-through time, is entirely controlled by imperfections in the system. Increasing the strength of imperfections dramatically reduces the snap-through time. Analytical expressions for the snap-through times are presented for limit-point and bifurcation buckling. Our Letter suggests that natural curvature and deliberately introduced imperfections can be used to tune the snap-through dynamics of new functional materials.