Chaotic motion of a shallow arch

In shallow arches, the phenomena of ";nap-through" instability is well established. In this paper, the effect of small external periodic excitation on the dynamic response of a shallow arch is examined. The stability and Sifurcations of the periodic motions near the stable equilibrium states of the shallow arch are examined l~sing the method of averaging. It is shown that as the amplitude and frequency of the excitation are varied, the nonlinear system can either undergo an unstable subcritical or stable supercritical bifurcation depending on the +?xcitation frequency. In addition, it is shown thit such a nonlinear system with three,d~mensions can exhibit chaotic oscillations. The method of Melnikov is used to determine the analytical results for the critical parameters at which the dynamicdl system possesses a horseshoe chaos. The results obtained by the Melnikov technique are compared to those obtained by numerical integration.