Large amplitude three-dimensional free vibrations of inclined sagged elastic cables

The nonlinear characteristics in the large amplitude three-dimensional free vibrations of inclined sagged elastic cables are investigated. A model formulation which is not limited to cables having small sag-to-span ratios and takes into account the axial deformation effect is considered. Based on a multi-degree-of-freedom cable model, a finite difference discretization is employed within a numerical solution of the governing equations of three-dimensional coupled motion. Various numerical examples of arbitrarily inclined sagged cables with initial out-of-plane or in-plane motions are carried out for the case of a specified end tension. The major findings consist of highlighting the extent of two-and three-dimensional nonlinear couplings, the occurrence of nonlinear dynamic tensions, and the meaningfulness of modal transition phenomena ensuing from the activation of various internal resonance conditions. The influence of cable inclination on the nonlinear dynamic behavior is also evaluated. Comprehensive discussion and comparison of large amplitude free vibrations of horizontal and inclined sagged cables are presented.