G. Mustafa et A. Ertas, EXPERIMENTAL-EVIDENCE OF QUASI-PERIODICITY AND ITS BREAKDOWN IN THE COLUMN-PENDULUM OSCILLATOR, Journal of dynamic systems, measurement, and control, 117(2), 1995, pp. 218-225
A new vibration absorbing device is introduced for large flexible stru
ctures. The phase-space of the experimental system is reconstructed vi
a delay-coordinate embedding technique. Experimental dynamics indicate
that the motion is predominantly quasiperiodic, confirming the existe
nce of invariant tori. Within the quasiperiodic region, there are wind
ows 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 resul
ts in distortion of the invariant torus due to the resonance overlap.
Due to the resonance overlap, the return map extracted from the experi
mental data becomes noninvertible. Furthermore, a burst of frequencies
appears on the Fourier spectrum This scenario is similar to many expe
rimental observations of hydrodynamical instabilities; the breakup of
the tori in these experiments is related to the onset of turbulence.