Out-of-plane dynamic parametric instability of circular arches with elastic rotational restraints under a localized uniform radial periodic load

Out-of-plane dynamic instability of a circular arch with elastic rotational constraints under localized uniform radial periodic load is studied in this paper which has not been yet reported in the literature. In the out-of-plane dynamic instability analysis, the coupled equation of motion associated with lateral displacement and twist angle is derived by using an energy method and Hamiltonian principle. Then the mode shape functions of arches with different elastic rotational restraints are deduced and analytical solution for unstable regions with a period of 2T are obtained by using Bolotin's method. Finite element numerical analysis is employed to justify the dynamic unstable regions by frequency sweeping simulation and the results show a desirable agreement. It is found that when the flexibility of out-of-plane elastic rotational restraints decreases, the unstable region moves towards the direction of higher frequencies owing to the increase in rigidity of the arch, with the out-of-plane dynamic stability of the arch being improved. The load localized parameter significantly impacts the dynamic stability for the arches with various flexibility of out-of-plane restraints. These results give us a deep understanding of the instability mechanism of engineering structures with arches and provide insight into the effective design of arch structures.