Abstract
This study deals with the nonlinear dynamic behavior and the stability of a flexible cable structure with large sag subjected to the periodic excitation. The dynamic behavior of the flexible cable becomes unstable because of the restoring force of the gravity acting on the flexible cable. Both ends of the flexible cable are supported at the same height. One supporting end of the flexible cable is fixed rigidly, the other supporting end of the flexible cable is subjected to the periodic excitation in the vertical direction. We developed an analytical model of the flexible cable by using the finite segment method. This analytical model is divided into some rigid bodies which are connected by hinged joints. The each rigid body has the restoring force of gravity. From this analytical model, differential algebraic equations of the flexible cable are derived as a finite segment formulation. We calculated the nonlinear dynamic behavior and the parametric instability region by the numerical simulations. Moreover, the validity of the presented analytical model is verified by the experiments, and the nonlinear behavior and the parametric instability region of the flexible cable are discussed by the numerical simulations and the experiments.
