Nonlinear vibrations of suspended cables—Part II: Deterministic phenomena

Abstract

The present work is concerned with deterministic nonlinear phenomena arising in the finite-amplitude dynamics of elastic suspended cables. The underlying theoretical framework has been addressed in Part I of this Special Issue, where the mechanical system and its mathematical modeling have been presented, and different techniques for the analysis of nonlinear dynamics have been illustrated with reference to the suspended cable. Herein, we discuss the main features of system regular and complex response, and the associated bifurcational behavior. Nonlinear phenomena are considered separately for single-degree-of-freedom and multidegree-of-freedom cable models, by distinguishing between theoretical and experimental results and comparing them with each other. Regular and nonregular vibrations are considered either in the absence of internal resonance or under various internal/external, and possibly simultaneous, resonance conditions. The most robust classes of steady periodic motions, the relevant response scenarios in control parameter space, and the main features of multimodal interaction phenomena are summarized. Bifurcation and chaos phenomena are discussed for the single-dof model by analyzing the local and global features of steady nonregular dynamics. For the experimental model, the most meaningful scenarios of transition to chaos are illustrated, together with the properties of the ensuing quasiperiodic and chaotic attractors. Finally, the important issues of determining system dimensionality and identifying properly reduced-order theoretical models of cable are addressed. There are 185 references listed in this review article.