DYNAMICS AND BIFURCATIONS OF A COUPLED COLUMN-PENDULUM OSCILLATOR

This study deals with the dynamics of a large flexible column with a t ip mass-pendulum arrangement. The system is a conceptualization of a v ibration-absorbing device for flexible structures with tip appendages. The bifurcation diagrams of the averaged system indicate that the sys tem loses stability via two distinct routes; one leading to a saddle-n ode bifurcation, and the other to the Hopf bifurcation, indicating the existence of an invariant torus. Under the change of forcing amplitud e, these bifurcations coalesce. This phenomenon has important global r amifications, in the sense that the periodic modulations associated wi th the Hopf bifurcation tend to have an infinite period, a strong indi cator of existence of homoclinic orbits. The system also possesses iso lated solutions (the so-called ''isolas'') that form isolated loops bo unded away from zero. As the forcing amplitude is varied, the isolas a ppear, disappear or coalesce with the regular solution branches. The r esponse curves indicate that the column amplitude shows saturation and the pendulum acts as a vibration absorber. However, there is also a f requency range over which a reverse flow of energy occurs, where the p endulum shows reduced amplitude at the cost of large amplitudes of the column. The experimental dynamics shows that the periodic motion give s rise to a quasi-periodic response, confirming the existence of tori. Within the quasi-periodic region, there are windows containing intric ate webs of mode-locked periodic responses. An increase in the force a mplitude causes the tori to break up, a phenomenon similar to the onse t of turbulence in hydrodynamics.