Dynamic buckling of shallow pin-ended arches under a sudden central concentrated load

When a shallow arch is subjected to an in-plane load that is applied suddenly, the arch will oscillate about an equilibrium position due to the kinetic energy imparted to the arch by the sudden load. If the suddenly applied load is sufficient large, the motion of the arch may reach an unstable equilibrium position, leading to dynamic buckling of the arch. This paper presents a study of the dynamic in-plane buckling of a shallow pin-ended circular arch under a central radial load that is applied suddenly with infinite duration. The method of conservation of energy is used to establish the criterion for dynamic buckling of the shallow pin-ended arch and analytical solutions for the lower and upper dynamic buckling loads of the arch under this sudden central load with infinite duration are obtained. It is found that the dynamic buckling loads of a shallow pin-ended arch under a sudden central load with infinite duration are lower than its static buckling loads, and that the dynamic buckling load increases with an increase of a dimensionless arch geometric parameter that is introduced. The effect of static preloading on the dynamic buckling of a shallow pin-ended arch is also investigated. It is found that the pre-applied static load decreases its dynamic buckling loads, but increases the sum of the pre-applied load and the dynamic buckling load.