The Periodic Solution and Numerical Simulations for Iced Cable System

In this paper, the periodic behavior of iced cable in the case of the in-plane fundamental parametric resonance-principal resonance, out-of-plane principal parametric resonance-principal resonance, and in 1:2 internal resonances is investigated. The sufficient condition for the existence of the periodic solutions about the system is obtained through using Melnikov function and Poincare mapping, then the stability of periodic solution is investigated by using blow-up transformations and the average method. Numerical simulations are performed to verify the analytical predictions and get three groups of diagrams.