Non-Linear Dynamic Analysis on a Continuum Suspension Bridge Model with Spatial Layout of Main Cables

This study proposes an approach to set up a continuum full bridge model with spatially inclined cables based on the Hamilton principle. The dynamic governing functions, considering the geometric non-linearities of cables and deck, represent simultaneously the vertical motion of deck and vertical–horizontal motion of cable. With the comparison of the modal properties obtained from the model to those from the accurate model, results show that the proposed model is capable of accurately simulating the modal properties. The primary resonance responses and corresponding frequency-response curves are obtained through the multiple-scale-method. A finite element (FE) model is established, and the corresponding non-linear dynamic analysis in time domain is conducted. Comparing the results from two models, it can be checked that the proposed model is reliable. According to the results of the proposed model, it is found that the second-order shape functions (SOSFs) play a significant role in the system response. Once the non-linear vibration of the bridge becomes significant only considering the excited mode with using the classical Galerkin decomposition cannot correctly predict the structure response. The SOSFs can be classified into stationary and vibrating components. The vibrating component can deviate the time-series of response from the harmonic wave, and the stationary component directly determines the mean value of the time-series.