Novel vibration suppression of spinning periodically acoustic black hole pipes based on the band-gap mechanism

Abstract

Due to the fluid-structure interaction, external perturbation, and internal fluid, etc., the terrible vibration and noise emission in pipes conveying fluid may make the engineering structures facilitate to be instability, serious failure, and catastrophic destruction. In this work, inspired by the band gaps formation of photonic crystal (PC) and the wave attenuation in acoustic black hole (ABH), four novel types of periodic pipes conveying fluid including the unidirectional and axisymmetric ABH cells are proposed and used as basic models to analyze the mechanism of band gap formation. Considering a novel spinning two-dimensional (2D) PC model, the governing and dispersion equations of the proposed pipes conveying fluid are established based on the Timoshenko beam theory. By adopting the spectral element method (SEM) compared with the transfer matrix method (TMM), as well as introducing the Bloch theorem, the wave propagation mechanism in these spinning periodic ABH pipes conveying fluid is disclosed through investigating the frequency response, flexible wave shapes, energy transfer mode and BGs distribution. We find that, in the case of periodic pipes conveying fluid, the concentration of kinetic energy at the junction of the sub-cell can enhance Bragg scattering, which leads to the formation of band gaps (BGs), while the pass bands are generated due to the drastic variation of wave mode induced by the resonance in the strain energy. Based on the BGs mechanism, the parameter analysis is carried out to indicate the vibration suppression of the spinning periodic pipes decrease periodically with the spinning speed. More importantly, by adjusting the ABH geometric parameters, it is found that all four types of periodic pipes conveying fluid can generate lower-frequency and broader BGs, which further leads to weaken the disadvantage effect of the spinning speed on vibration self-suppression of the pipe system. Based on the above analysis of the mechanism and parameters of BG's formation, a novel vibration control method with the cooperation of the periodic structure and the ABH effect is developed. The study provides a novel design idea of the PC development in the axially moving continuum, which may be beneficial for controlling the vibration of engineering fluid-conveying devices.