In-plane stability of preloaded shallow arches against dynamic snap-through accounting for rotational end restraints

Because the non-linear equilibrium path of a shallow arch has unstable branches, when the arch is subjected to a suddenly-applied load, it may lose its stability by dynamic snap-through owing to excessive oscillations reaching its unstable branch. In practice, arches are usually subjected to a certain level of static loading before the sudden load is applied. The static load may have a profound influence on the dynamic snap-though instability of the arch. In addition, the rotational end restraints of an arch provided by adjacent structural members or/and elastic foundations have significant influences on the geometric non-linearity of the arch, and consequently they influence its stability against dynamic snap-through under a suddenly-applied load. An energy approach is used to derive the dynamic snap-through buckling loads of statically preloaded shallow circular arches having rotational end restraints under a suddenly-applied uniform radial load. It is found that the statically preloaded arches can be susceptible to dynamic snap-through buckling. It is also found that the dynamic buckling loads of the arches are influenced significantly by the magnitude and difference of the relative flexibility of the rotational end restraints. Arches having equal rotational end restraints may have an upper and a lower dynamic buckling loads, whereas arches having unequal rotational end restraints have only a unique dynamic buckling load.