Pipe systems are commonly used in the process and power industries to transport fluid from one terminal to others. Propagation behaviour of lateral flexural waves in a pipe coupled with periodic rack structure is investigated. The pipe-rack system considered in this study is a practical case and is realized as a pipe on periodic elastic supports, while a pipe on simple and without supports represents special cases when the rack stiffness leads to extreme values. The propagation constant relations in terms of frequency are derived using Bloch–Floquet theorem which are successively verified with finite element models. The results show that a pipe with rack creates a narrow locally resonant band gap in low-frequency range which is caused by the first natural mode of the rack. Conversely, a pipe on simple supports entails only Bragg-type band gaps, while a pipe without supports carries no band gap. For tuning the band gap properties, a two-degrees-of-freedom lateral localized resonator is attached to the centre of each unit cell of the pipe. It is found that certain frequency ranges in the targeted pass bands are effectively controlled by the resonator. Furthermore, the effect of various resonator parameters, i.e. mass ratio, stiffness and damping, on band gaps is examined. It is observed that the band gaps are vanished when damping is introduced in the system. The results show a promising way to flexural vibration control of a periodic piping system with various boundary conditions.

管道系统通常用于过程和电力行业，以将流体从一个终端输送到其他终端。研究了具有周期性齿条结构的管道中横向弯曲波的传播行为。本研究中考虑的管架系统是一个实际案例，并被实现为周期性弹性支撑上的管道，而简单和没有支撑的管道代表了机架刚度导致极端值的特殊情况。使用 Bloch-Floquet 定理推导出频率方面的传播常数关系，该定理已通过有限元模型连续验证。结果表明，带有齿条的管道在低频范围内会产生狭窄的局部谐振带隙，这是由齿条的第一固有模式引起的。相反，简单支撑上的管道只需要布拉格型带隙，而没有支撑的管道没有带隙。为了调整带隙特性，将一个二自由度横向局部谐振器连接到管道的每个单元的中心。发现目标通带中的某些频率范围被谐振器有效地控制。此外，还检查了各种谐振器参数（即质量比、刚度和阻尼）对带隙的影响。观察到当系统中引入阻尼时带隙消失。结果显示了一种对具有各种边界条件的周期性管道系统进行弯曲振动控制的有前途的方法。发现目标通带中的某些频率范围被谐振器有效地控制。此外，还检查了各种谐振器参数（即质量比、刚度和阻尼）对带隙的影响。观察到当系统中引入阻尼时带隙消失。结果显示了一种对具有各种边界条件的周期性管道系统进行弯曲振动控制的有前途的方法。发现目标通带中的某些频率范围被谐振器有效地控制。此外，还检查了各种谐振器参数（即质量比、刚度和阻尼）对带隙的影响。观察到当系统中引入阻尼时带隙消失。结果显示了一种对具有各种边界条件的周期性管道系统进行弯曲振动控制的有前途的方法。