CHAOTIC DYNAMICS OF SHALLOW ARCH STRUCTURES UNDER 1 2-RESONANCE/

The global dynamics of a shallow arch structure subjected to a spatial ly and temporally varying force is investigated under the conditions o f principal subharmonic resonance and one-to-two internal resonance ne ar single mode periodic motions. We describe the mechanism leading to chaotic behavior in the class of systems under consideration. In this paper, a higher-dimensional, Melnikov-type perturbation method is used to analytically show that the arch structure, in the absence of any d issipation mechanism, may exhibit chaotic dynamics in the sense of Sma le horseshoe for the one-to-two internal resonance case. These chaotic motions result from the existence of orbits heteroclinic to a normall y hyperbolic invariant torus, which corresponds to the hyperbolic peri odic orbit in the averaged system. In this case, the presence of small dissipation causes the phase dow to be attracted towards the trivial solution. Numerical simulations are also performed to confirm the theo retical predictions and hence the existence of complicated dynamics in the shallow arch system.