NONLINEAR DYNAMICS OF A SHALLOW ARCH UNDER PERIODIC EXCITATION .1. 1 2 INTERNAL RESONANCE/

The weakly non-linear resonance response of a two-degree-of-freedom sh allow arch subjected to simple harmonic excitation is examined in deta il for the case of 1:2 internal resonance. The method of averaging is used to yield a set of autonomous equations of the first-order approxi mations to the response of the system. The averaged equations are then examined to determine their bifurcation behavior. Our analysis indica tes that by varying the detuning parameters from the exact external an d internal resonance conditions, the coupled mode response can undergo a Hopf bifurcation to limit cycle motion. It is also shown that the l imit cycles quickly undergo period-doubling bifurcation, giving rise t o chaos. In order to study the global bifurcation behavior, the Melnik ov method is used to determine the analytical results for the critical parameter at which the dynamical system possesses a Smale horseshoe t ype of chaos.