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 period ic excitation with internal resonance is explored in detail. The parametric plane is then divided into different types of regions by the transition bo undaries according to the types of the steady state solutions. A time-integ ration scheme is used to find the numerical solutions in these regions, whi ch agree with the analytic results. Finally, numerical simulation is also a pplied 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. (C) 2000 Academic Press.