ANALYSIS OF NON-LINEAR DYNAMICS AND BIFURCATIONS OF A SHALLOW ARCH SUBJECTED TO PERIODIC EXCITATION WITH INTERNAL RESONANCE

In this paper, the dynamical behavior of a shallow arch subjected to periodic excitation with internal resonance is explored in detail. The parametric plane is then divided into different types of regions by the transition boundaries according to the types of the steady state solutions. A time-integration scheme is used to find the numerical solutions in these regions, which agree with the analytic results. Finally, numerical simulation is also applied to obtain double-period cascading bifurcations leading to chaos and the steady state period-3 solution is shown in the chaos region in the end.