平面外振动周期性高架桥失谐局部化问题分析

考虑周期性高架桥结构由桥墩及两相邻的水平梁组成,分析平面外振动失谐引起局部化现象。首先建立水平梁-桥墩连接处的传递矩阵,结合Wolf算法推导描述周期性高架桥波场局部化的Lyapunov正指数,并讨论高架桥结构的桥墩高度、桥梁跨度失谐及材料阻尼变化对描述局部化因子的Lyapunov指数影响。计算结果表明:低频时桥墩高度及桥梁跨度失谐对Lyapunov指数几乎没有影响,而随频率增加,周期高架桥结构失谐引起局部化现象明显;在通带域,振动波局部化更容易受结构材料阻尼变化的影响;在禁带域,高架桥的桥墩高度、桥梁跨度失谐对振动局部化影响要大于结构材料阻尼。

Wave Localization in a Disordered Periodic Viaduct Undergoing Out-of-plane Vibration

Wave localization in a disordered periodic viaduct(DPV) undergoing out-of plane vibration is investigated.To this end, each span of the viaduct is simplified as a unit composed of a pier and two longitudinal beams.To investigate the wave localization in the disordered periodic viaduct, first the transfer matrix for the junction connecting two beams and one pier in one span of the viaduct is derived. Based on the transfer matrix for each span of the viaduct, the wave transfer matrix for each span is then constructed. By using the wave transfer matrices and Wolf''s algorithm, the Lyapunov exponents for the wave localization in the viaduct can be determined. Using the proposed model, the influences of the pier-height and beam-length disorders on the wave localization are examined. In addition, the interactive effect of the damping in the pier and beam materials and the pier-height and beam-length disorders on the wave localization in a disordered viaduct are analyzed. Numeric results show that when pier-height and beam-length disorders occur, the Lyapunov exponents are almost unaffected by the lower frequency disorders. However, at increasing frequencies, the influences of the pier-height and beam-length disorders on the Lyapunov exponents becomes more significant. For the assumed parameters of the viaduct, in pass-bands, the damping of the piers and beams has a larger influence on the wave localization than the pier-height and beam-length disorders, while in the stop-bands, the disorders have a more pronounced influence on the wave localization than the damping.