Abstract: The nonlinear dynamic analysis for the coupled structure of cable-stayed beam subject to fully parametric excitation is provided. The mechanical model of cable-stayed beam is established. The non-linear partial differential equations are derived for a coupled structure of cable-stayed beam subject to fully parametric excitation by using Hamilton principle. The Galerkin method is adopted to obtain ordinary differential equations of the coupling motion in stayed system. The non-linear vibration of coupled structure is analyzed with the help of multi-scale method. By means of Runge-Kutta method, the numerical solutions of differential equations are obtained which indicate that there is serious parametric resonance when the cable-stayed beam frequency ratio is 2:1. Through the analysis of relative response curves, the damping parameters are concluded which have significant influence on the coupling vibration of the cable-stayed beam. The conclusion having actual meaning to engineering is proposed.

Key words: Coupling of cable-stayed beam, Galerkin method, Multi-scale method, Non-linear vibration, Parametric excitation