Nonlinear Vibration of Coupled Structure of Cable-stayed Beam

Abstract:

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

Key words:coupling of cable-stayed beam; non-linear vibration; Galerkin method; multi-scale method; 1∶2 internal resonance