Bifurcation analysis of an arch structure with parametric and forced excitation

The 12 subharmonic bifurcation and universal unfolding problems are discussed for an arch structure with parametric and forced excitation in this paper. The amplitude–frequency curve and some dynamical behavior have been shown for this class of problems by Liu et al. Here, by means of singularity theory, in the case of strict 1:2 internal resonance, the bifurcation behavior of the amplitude with respect to a parameter (which is related to the amplitude of the live load imposed on the arch structures) is studied. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, 20 forms of two parameter unfoldings with some constraints are studied. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper present some new dynamic buckling patterns and abundant bifurcation phenomena.