Retuning the disordered periodic structures by sorting unit cells: Numerical analyses and experimental studies

Periodic structures feature frequency band gaps in which the propagation of certain waves will be attenuated. Therefore, they are widely applied in the vibration control of structures. The premise of this theory is that the structure should be perfectly periodic. However, this must be broken more or less due to inevitable deviations, leading structures to disorder. The vibration reduction performance can be significantly altered by the disorder, as reported by various authors. Moreover, the disorder pattern plays an important role in such a performance change. In this paper, we study the influence of the disorder patterns and explore a general permutation to retune the disordered periodic structures which means to reduce the deviation of the dynamic characteristics between the nominal and disordered structures. This research is conducted through three stages. In the first stage, a diatomic lumped-mass model is used. We study the implication of the disorder and propose a sorting strategy inspired by global sensitivity analysis (GSA). In the second stage, the sorting strategy is corroborated with numerical simulations by a finite element (FE) model of beam. We use the wave finite element method (WFEM) to calculate the band gaps. A thousand samples are generated randomly to test the sorting strategy and the contrarian strategy. In the third stage, the sorting strategy is verified by an experimental structure of beam. We set up an experimental system and scheme to measure and analyze the effects of the strategy for 5 groups of experiments. We show that vibration suppression may deteriorate statistically due to disorder for periodic structures. Specifically, vibration mitigation is most sensitive to the deviation in the first unit cell from the excitation. Inspired by this finding, a retuning strategy is proposed for the first time, i.e. the unit cell with the smallest deviation should be arranged in the position nearest to the excitation. The results in all stages show that the strategy can significantly improve the similarity of the dynamic characteristics between the nominal and disordered structures.