Lateral flexural vibration reduction in a periodic piping system enhanced with two-degrees-of-freedom resonators

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.