Three-to-one internal resonance analysis for a suspension bridge with spatial cable through a continuum model

Abstract

Abstract 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.