失谐周期盾构隧道结构的弯曲波动局部化

Flexural wave localization in disordered periodic jointed tunnels

针对随机失谐周期接头盾构隧道结构的波动局部化特性进行了研究。将盾构隧道模拟为弹性地基上通过环间接头连接的周期管梁模型,基于弹性地基上均匀管梁的横向波动微分方程及接头的平衡方程,推导了结构中各胞元的动态刚度矩阵,进而利用传递矩阵法建立了相邻胞元间的传递矩阵。将随机失谐参数引入到周期结构中,根据Wolf算法,采用局部化因子计算了不同控制参数对弯曲波动局部化特性的影响。通过对失谐周期隧道的一系列算例分析表明,弹性地基上的均匀隧道存在一个临界频率,当波动频率小于该临界频率时,弯曲波的传播始终是衰减的。同时,弹性地基作用使得周期隧道弯曲振动波的禁带频率有所提高。失谐周期隧道将出现波动局部化现象。随着失谐程度的增加,结构的波动局部化程度增强。对于同一失谐程度,波动局部化现象在高频段更为显著。进一步,采用有限元方法验证了所提出周期盾构隧道模型的正确性。

Flexural wave localization in the disordered periodic jointed tunnel is investigated.The periodic jointed tunnel is ap-proximated as a pipe-beam model with periodic joints on elastic foundations.By using the differential equations governing the flexural vibration of the pipe-beam on elastic foundations as well as the force equilibrium of the joints,the transfer matrix of the periodic jointed tunnel is derived based on the dynamic stiffness matrix.A random disorder is introduced in the disordered peri-odic jointed tunnel,and the localization factors are calculated to examine the wave localization according to the Wolf’s algo-rithm.The effects of various controlling parameters on the wave localization characteristics of the disordered periodic structures are assessed through a comprehensive set of numerical case studies.The obtained results show that the flexural wave is always attenuated when the frequency is less than some critical frequency of a uniform tunnel on elastic foundations.As the level of disorder increases,the localization degree is strengthened.For the same disorder level,the phenomenon of wave localization is more pronounced at the high frequency range.The validity of the proposed methodology is verified by the finite element simula-tions at the end of this paper.