Dynamic response of a shallow arch under end moments

In this paper we study the dynamic response of a pinned shallow arch subjected to a pair of equal and opposite end moments suddenly. An experimental setup is designed to measure both the static deflection and dynamic response of the loaded arch. The dynamic buckling load as a function of the rise parameter is of particular interest. In order to theoretically identify the necessary and sufficient condition for dynamic snap-through, an accurate estimate of the system damping is required. This, however, proves to be a difficult task. A more practical approach is to adopt a sufficient condition which ensures that the arch will be safe from dynamic snapping. This condition leads to a lower bound of the dynamic critical load. As long as the end moments are smaller than this lower bound, it is guaranteed that the arch will not snap dynamically no matter what the system damping may be. For an arch with rise parameter greater than 6.55, it is shown that a closed-form expression of this lower bound of dynamic critical load can be derived. This simple formula should prove useful to design engineers.