Characterizing bifurcations and classes of motion in the transition to chaos through 3D-tori of a continuous experimental system in solid mechanics

The dynamics of a continuous experimental system exhibiting quasiperiodic transition to chaos has been investigated. An elastic cable/mass system hanging at in-phase vertically moving supports is considered, with vibrational parameters in the neighbourhood of external and internal resonance conditions adjusted to be able to introduce three-torus dynamics. Measurements of the nonregular response are made in frequency ranges including primary resonance of the first symmetric in-plane mode of the cable. Quantitative characterisation of regular and nonregular attractors and of the configuration variables involved in the motion is made by means of delay-embedding technique and proper orthogonal decomposition of spatio-temporal how. Attention is devoted to analyse in-depth the scenario of transition to chaos exhibited by the model. Steady quasiperiodic motions on three-tori, partial and full phase-locking of the flow, and chaotic attractors are observed. In spite of the dynamics variedness, the systematic characterisation of the response allows us to set the bifurcation behaviour of the experimental system in the framework of theoretic/numeric transition to chaos through three-dimensional tori. (C) 2000 Elsevier Science B.V. All rights reserved.