考虑模态振型影响的斜拉桥非线性内共振能量转换研究

This study investigates the complex mechanism of nonlinear vibrations induced by local-global modal interactions in cable-stayed bridges. Through numerical simulations and experiments on a cable-beam coupled structure, we systematically examined the energy transfer processes and characteristics of 1∶1 internal resonance considering the influence of global modal shapes. First, a cable-beam coupled model was established using discrete parametric beam segments, considering the geometric nonlinearity caused by the cable's sag. Based on the cable-beam dynamic conditions, differential governing equations were obtained using the D'Alembert principle and algebraically reduced using the finite difference method. Moreover, ordinary differential governing equations of infinite dimensionality were derived using separation and modal drag methods. Subsequently, the mechanism of the resonance energy transfer was further analyzed based on the numerical simulations and laboratory experiments. The results show that when internal resonance occurs, the cable-beam anchorage particle is the main path for periodic resonance energy transfer. The amplitude of the global modal shape significantly influences the resonance energy transfer between the cable and the beam. Specifically, when the cables are anchored at global modal stagnation points and satisfy the proportional conditions of the modal frequency, the energy transmission between the cables and the beam is inhibited, preventing internal resonance in the structure. During multiple internal resonances, the first- and second-order cable vibrations remain independent of each other. The resonance frequency conditions are validated as the premise of the internal resonance, whereas the periodic energy transfer between the local and global modes is the fundamental cause. Furthermore, the proposed modal participation factor at the cable-beam anchor point is the critical factor that influences the energy transfer.