Nonlinear interaction of a parametrically-excited coupled column-pendulum oscillator

A new vibration absorbing device is introduced for large flexible structures. The bifurcation diagrams obtained for the averaged system, indicate that the system loses stability via two distinct routes. One leading to a saddle-node bifurcation, normally associated with the jump phenomena. The second instability is due to the Hopf bifurcation, that results in amplitude modulated motion of the oscillator. A parameter range has been identified where these bifurcations coalesce. This phenomenon is a strong indicator of existence of homoclinic orbits. In addition to the regular solution branches, that bifurcate from the zero solution, the system also possesses isolated solutions (the so-called 'isolas') that form isolated loops bounded away from zero. As the forcing amplitude is varied, the isolas appear, disappear or coalesce with the regular solution branches. The response curves indicate that the column amplitude shows saturation. The pendulum acts as a vibration absorber over a range of frequency where the column response is saturated. However, there is also a frequency range over which a reverse flow of energy occurs, where the pendulum shows reduced amplitude at the cost of large amplitudes of the column.