Experimental Evidence of Quasiperiodicity and Its Breakdown in the Column-Pendulum Oscillator

Abstract

A new vibration absorbing device is introduced for large flexible structures. The phase-space of the experimental system is reconstructed via delay-coordinate embedding technique. Experimental dynamics indicate that the motion is predominantly quasiperiodic, confirming the existence of invariant tori. Within the quasi-periodic region, there are windows containing intricate webs of phase-locked periodic responses. The quasiperiodic and the phase-locked responses are clearly visualized on the cover of the torus. Increase in the amplitude of excitation results in distortion of the invariant torus due to the resonance overlap. Due to the resonance overlap, the return map extracted from the experimental data becomes noninvertible. Furthermore, a burst of frequencies appears on the Fourier spectrum. This scenario is similar to many experimental observations of hydrodynamical instabilities; the breakup of the tori in these experiments is related to the onset of turbulence.