Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system

An experimental model of an elastic cable/mass hanging at in-phase or out-o f-phase vertically moving supports is considered. System parameters are adj usted to produce two different conditions of multiple internal resonance. N onregular dynamics are analyzed in various frequency ranges including meani ngful external resonance conditions. Attention is devoted to characterizati on of system dimensionality in terms of both time and spatial complexity. T he aims of this paper are (i) to give a general overview of the richness an d robustness of different (quasiperiodic and homoclinic) bifurcation scenar ios to chaos in various regions of the control parameter space, (ii) to cha racterize steady nonregular response through delay-embedding technique for attractor reconstruction and proper orthogonal decomposition of spatio-temp oral flow and (iii) to identify spatial configuration variables (experiment al eigenfunctions) contributing mostly to nonregular dynamics, thus obtaini ng hints about possible reduced models for reproducing complex regimes. Sys tem dimensionality will be evaluated both by relating the dimension of attr actors to the dimension of the linear phase space, and from the dominating proper orthogonal modes. (C) 2001 Elsevier Science Ltd. All rights reserved .