Chaotic motion of shallow arch structures under 1:1 internal resonance

The present study investigates the global bifurcations present in the motion of the shallow arch structure subjected to a spatially and temporally varying load under the conditions of principal subharmonic resonance and one-to-one internal resonance near single-mode periodic motions. Unlike the case examined in a companion paper by the writers, the effect of dissipation is also included in the present study of the global dynamics. By using a perturbation technique attributed to Kovačič and Wiggins we show the existence of Silnikov-type homoclinic orbit to a saddle-focus fixed point in the perturbed system, and consequently the chaotic behavior. The results are also interpreted in terms of the physical dynamics of the shallow arch system.