Abstract
The third-order subharmonic oscillations in weakly non-linear cyclic symmetric structures with multiple degrees of freedom are studied. These strongly coupled cyclic structures, in their linear approximation, are known to possess pairwise double-degenerate natural frequencies with orthogonal normal modes. The asymptotic method of averaging is used to study the nonlinear interactions between the pairs of modes with nearly identical natural frequencies when the external excitation is nearly three times the natural frequency of the modes being excited. A careful local bifurcation analysis of the averaged equations is conducted to study the effects of frequency mistuning and excitation amplitudes, as well as the modal damping in the system. Subharmonic standing and travelling wave type solutions, Hopf bifurcation from travelling wave solutions to quasiperiodic responses, period-doubling bifurcations, and Silnikov type chaos are found to exist in the averaged system.
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