桩基础支撑的周期性高架桥结构的缺陷态研究

Research on Defect State of the Structure of a Pile-supported Periodic Viaduct

基于传递矩阵方法,对桩基础支撑的周期性高架桥结构在面外振动下的缺陷态进行研究。为考虑高架桥上部结构与桩基础的耦合,首先建立分析桩-土相互作用的边界元模型。利用上述边界元模型,梁和墩的传递矩阵,梁-梁-墩接头处的联结条件及传递矩阵方法,推导了高架桥单跨的传递矩阵。缺陷周期性高架桥结构的缺陷态可通过标准跨和缺陷跨的传递矩阵及超原胞方法求解得到。超原胞的能带显示,缺陷高架桥存在缺陷态;当频率为缺陷态频率时,超原胞的缺陷波模态表明波动会局域在高架桥的缺陷跨处。

Based on transfer matrix method, the defect state of a pile-supported periodic viaduct undergoing out-of-plane vibration was studied. To account for the coupling between the superstructure of the viaduct and the pile foundations, a boundary element model for the analysis of the pile-soil interaction was established at first. And then by using above-mentioned boundary element model, by using the transfer matrices between the beams and piers, by using the joint conditions at the junction of beam- beam-pier and by using the transfer matrix method, the transfer matrix for each span of the viaduct is deduced. And the defect state of the defected periodic viaduct structure can be obtained by solving the transfer matrices of the standard and defected spans as well as by using the super-cell method. The energy band of the super-cell demonstrates that there is defect state in the defected viaduct. Moreover, when the frequency is of the defect state frequency, the defect state wave mode of the super-cell manifests that the fluctuations may localize at the defected span of the viaduct.