SUBHARMONIC OSCILLATIONS IN HARMONICALLY EXCITED MECHANICAL SYSTEMS WITH CYCLIC SYMMETRY

The third-order subharmonic oscillations in weakly non-linear cyclic s ymmetric structures with multiple degrees of freedom are studied. Thes e strongly coupled cyclic structures, in their linear approximation, a re known to possess pairwise double-degenerate natural frequencies wit h orthogonal normal modes. The asymptotic method of averaging is used to study the nonlinear interactions between the pairs of modes with ne arly identical natural frequencies when the external excitation is nea rly three times the natural frequency of the modes being excited. A ca reful local bifurcation analysis of the averaged equations is conducte d to study the effects of frequency mistuning and excitation amplitude s, as well as the modal damping in the system. Subharmonic standing an d traveling wave type solutions, Hopf bifurcation from traveling wave solutions to quasiperiodic responses, period-doubling bifurcations, an d Silnikov type chaos are found to exist in the averaged system. (C) 1 997 Academic Press Limited.