Nonlinear Dynamic Analysis of Spatially Suspended Elastic Catenary Cable with Finite Element Method

This paper investigates the dynamic behavior of a cable considering geometrical nonlinearity due to the sagging effect, based on the elastic catenary cable thoery. The finite element method has been limited in application to the dynamic analysis of a cable element because its displacement interpolation function can not be obtained from the boundary conditions. This paper proposes a derivation of the interpolation function for spatially suspended catenary cable, using the flexibility matrix. Equations for the compatibility conditions of a catenary cable are derived under mutiple concentrated loads within an element. Also, self-weight and other vairous types of distributed load imposed within an element are discritized with equivalent concentrated loads at multiple Gaussian points. Dynamic inertia and damping forces along the cable profile are assumed to be distributed according to the developed interpolation functions so that internal forces are evaluated directly from the compatibility equations and flexiblity matrix. The proposed element is verified through an experiment testing the free vibration of a suspension cable, and the dynamic bahevior of a suspension cable is compared with the ABAQUS beam element where three-dimensional support excitations are imposed.