Nonlinear vibration of coupled structure of cable-stayed beam

Based on a series of partial differential equations describing the effect of curvature of the main cables and deformation of the stay cables on the structure, the non-linear ordinary differential equations of the first order approximation on time-domain are obtained by Galerkin method and studied by multi-scale method. An analysis is made of the principal resonance and 1:2 internal resonance. The analytical solutions of the first order approximation and the vibration amplitude response curves for the amplitude of excitation as a parameter are derived. The results indicate the first order approximate analytical solutions have a higher accuracy. In the internal resonance condition, there are jump phenomena of the vibration amplitudes of the main cables and the beam. But the low-order resonance bifurcation values of the jump phenomena are less than the high-order resonance bifurcation values, which indicates that the low-frequency resonance vibration is easier to generate substantial vibrations than the low-frequency. The study results are significant for engineering applications.