Nonlinear vibration of suspension bridge is a topic requiring comprehensive investigation. This study is focused on the internal resonance of the suspension bridge consisting of spatially inclined main cables and hangers by proposing a mathematic full bridge model. The vertical vibration of the bridge deck is studied. Specifically, the dynamic governing functions of this model can consider the geometric non-linearity of cables and deck. Firstly, the modal property of the continuum model is investigated, and the scenarios of modal frequency ratio between different modes equals to 3:1 are obtained. Then, the 3:1 internal resonances between two lowest symmetric or asymmetric modes with the external harmonic excitation are investigated by the Multiple Scales Method. The corresponding modulation equations explaining the internal resonance of two modes are obtained and solved by pseudo-arc-length method for exploring the nonlinear dynamic behaviors. The internal resonance is discussed with various detuning parameters. Some novel and interesting conclusions have been made. Knowledge of such possible occurrences can be beneficial in the design of the bridge structure.

悬索桥的非线性振动是一个需要综合研究的课题。本研究通过提出数学全桥模型，重点研究由空间倾斜的主缆和吊架组成的悬索桥的内部共振。研究了桥面板的竖向振动。具体来说，该模型的动态控制函数可以考虑缆索和甲板的几何非线性。首先研究了连续介质模型的模态特性，得到了不同模态间模态频率比等于3:1的场景。然后，两个最低对称或不对称模式之间的 3:1 内部共振与外部通过多尺度方法研究谐波激励。得到解释两种模式内共振的相应调制方程，并通过伪弧长方法求解，以探索非线性动力学行为。用各种失谐参数讨论了内部共振。得出了一些新颖有趣的结论。了解此类可能发生的情况有助于桥梁结构的设计。