Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables

• Published in: Journal of sound and vibration 2004-01, Vol.269 (3), p.823-852
• Main Authors: Srinil, Narakorn, Rega, Giuseppe, Chucheepsakul, Somchai
• Format: Article
• Language: English
• Subjects: Applied sciences; Buildings. Public works; Computation methods. Tables. Charts; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural analysis. Stresses; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(03)00137-8

This paper presents a model formulation capable of analyzing large-amplitude free vibrations of a suspended cable in three dimensions. The virtual work-energy functional is used to obtain the non-linear equations of three-dimensional motion. The formulation is not restricted to cables having small sag-to-span ratios, and is conveniently applied for the case of a specified end tension. The axial extensibility effect is also included in order to obtain accurate results. Based on a multi-degree-of-freedom model, numerical procedures are implemented to solve both spatial and temporal problems. Various numerical examples of arbitrarily sagged cables with large-amplitude initial conditions are carried out to highlight some outstanding features of cable non-linear dynamics by accounting also for internal resonance phenomena. Non-linear coupling between three- and two-dimensional motions, and non-linear cable tension responses are analyzed. For specific cables, modal transition phenomena taking place during in-plane vibrations and ensuing from occurrence of a dominant internal resonance are observed. When only a single mode is initiated, a higher or lower mode can be accommodated into the responses, making cable spatial shapes hybrid in some time intervals.