Multiple internal resonances and modal interaction processes of a cable-stayed bridge physical model subjected to an invariant single-excitation

There exist complex internal resonances in cable-stayed bridges. In order to study multiple internal resonances under the excitation of an invariant single-excitation and to ascertain the modal interaction processes, a nonlinear dynamic experiment of cable-stayed bridge was carried out. The modal parameters of the experimental physical model were evaluated by two finite element models (the OECS and MECS). Mode shapes were classified and compared to distinguish the in-plane and out-of-plane as well as the global, local and hybrid modes. Potential internal resonances were recognized by investigate the ratios between cable frequencies and the OECS frequencies. Then, attention was paid not only to the steady-state responses but also the coupling processes. It was observed that multiple internal resonances could induce large amplitude vibrations of the entire bridge, including the “beat vibration” of long-cables. Moreover, the sum of the two beat frequencies was equal to the excitation frequency. These phenomena were also found in transient analysis by the MECS finite element model. The interaction processes of the multi-mode resonances were revealed by separating vibration signals using the zero-phase-shift filtering technology and by precisely linking the observed modes to the MECS modes with frequency relations. Research shows that: the forced vibration, 2:1 local-local internal resonance and combined internal resonance had occurred simultaneously in the physical model.