Abstract: The complicated dynamics of shallow arch with periodic excitation for the case of 1:2 internal resonance is studied in this paper.It is pointed out that when the arch has an initial deflection,the first order and the second order modes can be in resonance and react to each other;therefore the energy can be transimitted between the low and high modes.The Hopf bifurcation solution after symmetric breaking can lead to chaos by a sequence of period-doubling bifurcations. The steady state periodic solutions can ...