考虑桥墩-水平梁间弹簧接头的周期性高架桥平面内振动能量带分析

Analysis of energy bands of periodic viaduct with pier-beam spring junction undergoing in-plane vibration

对无限多跨周期性高架桥结构的周期单元含一个桥墩、二个水平梁及三个连接弹簧,据Bernoulli-Euler梁及Bloch理论,推导具有水平梁-梁、水平梁-桥墩间弹簧接头传递矩阵,建立周期性高架桥结构平面内振动能量带特征方程。据该模型采用数值算例考察桥墩-水平梁刚度比、接头弹簧刚度等对周期性高架桥结构能量带分布特征影响。计算结果表明,具有水平梁-梁、水平梁-桥墩间弹簧接头的周期性高架桥结构发生平面内振动时,高架桥结构中存在与轴向压缩、横向剪切及弯曲振动对应的三类晶格波,即衰减较快且沿高架桥结构传播距离较短、只在某些频域能传播、除较小频率时难以传播外其它较宽频域均能传播。分析结果表明,高架桥结构设计时须保证结构基本主频不能落在较小频率区域,否则极易引起振动波能量集中,造成结构破坏。随周期性高架桥结构水平梁刚度、水平梁-梁接头弹簧刚度增大,沿高架桥结构传播的晶格波衰减会减慢,振动波能量沿高架桥结构会传播更远。

The periodic viaduct was modeled to be composed of an infinite number of spans,and each span was supposed to consist of one pier,two longitudinal beams and three linking springs.Based on the Bernoulli-Euler beam theory and Bloch theorem,a transfer matrix for the junction linking beams and pier was provided.The polynomial eigenvalue equation for the energy bands of the periodic viaduct undergoing in-plane motion was also derived.Based on the obtained eigenvalue equation,the energy bands of the periodic viaduct were solved.With the proposed model,the influences of the ratio of Young＇s modulus of beams to that of piers and the stiffness of springs on the energy bands of the periodic viaduct were investigated.The numerical results demonstrate that when the periodic viaduct with beam-beam and beam-pier spring junctions is undergoing in-plane motion, there exist three lattice waves corresponding to axial compression,transverse shear and bending vibration respectively：the first kind of lattice wave is a highly decaying wave and cannot propagate a long distance along the viaduct;the second kind of lattice wave can propagate only in some frequency ranges;and the third kind of lattice wave can propagate at most of frequencies except in a certain lower frequency range.As a result,it is crucial in the design stage to guarantee the dominant structural frequency of the viaduct not to be located within this low frequency range.Otherwise,most energy of seismic waves will be concentrated,which is dangerous for the viaduct.Moreover,with increasing the ratio of Young＇s modulus of the beams to that of the piers and the stiffness of the beam-beam spring,the attenuation of the lattice waves decreases significantly,implying that the wave can propagate a longer distance along the structures.