Multi-modal nonlinear dynamic response of cable-stayed beams with two-to-one internal resonance: Theory and experiments

In this study, the large-amplitude vibrations and nonlinear modal interactions of a cable-stayed beam under principal resonance excitation with theories and experiments are investigated, focusing on the 2:1 internal resonance between different modes. An accurate description of the interaction in the cable-stayed beam is obtained using the Hamilton variational principle, which leads to the derivation of the equations of motion for the system. A multi-modal discrete model of the cable-stayed beam is subsequently developed through a functional form approach. The method of multiple scales is employed to derive the averaged equations and second-order approximate displacement expressions. The equilibrium and dynamic responses of the cable-stayed beam under various principal resonance conditions are subsequently analyzed. The chaotic dynamics in the unstable region were analyzed based on numerical simulations, and the 2:1 internal resonance of the cable-stayed beam was investigated through experiments. It is found that the nonlinear response of the cable-stayed beam undergoes various bifurcations, displaying a rich spectrum of nonlinear dynamics. Finally, the effects of the interactions between cable and beam, the nonlinearity of beam are discussed.