Flexural band gaps and response attenuation of periodic piping systems enhanced with localized and distributed resonators.

Novel metamaterial concepts can be used to economically reduce flexural vibrations in coupled pipe-rack systems. Here, we model pipe on flexible supports as periodic systems and formulate dispersion relations using Floquet-Bloch theory which is verified by a finite element model. Owing to the flexibility of the coupled system, a narrow pass band is created in low frequency regime, in contrast to the case of pipe without any rack. Two types of vibration reduction mechanisms are investigated for pipe with different supports, i.e. simple and elastic support. In order to tune the band gap behaviour, lateral localized resonators are attached at the centre of each unit cell; conversely, the lateral distributed resonators are realized with a secondary pipe existing in the system. The results reveal that both Bragg and resonance type band gaps coexist in piping systems due to the presence of spatial periodicity and local resonance. Although, the response attenuation of a coupled pipe-rack system with distributed resonators is found to be little lower than the case with the localized one, the relatively low stiffness and damping values lead to cheaper solutions. Therefore, the proposed concept of distributed resonators represents a promising application in piping, power and process industries.