Sorting strategy to retune the disordered periodic structures regarding vibration reduction in band gaps

Abstract

Periodic structures exhibit frequency band gaps, in which the propagation of certain waves is attenuated. A periodic structure can be designed such that its band gaps cover the excitation frequencies and its vibration can be reduced. However, perfectly periodic structures do not exist in reality due to inevitable deviations in the material and geometric properties. The vibration reduction performance can be significantly altered by the disorder, as reported by various authors. Therefore, it is favorable to find approaches that can retune disordered structures to the best possible state. In this way, robust vibration reduction performance can be achieved. In this study, a sorting strategy is proposed to rearrange the disordered unit cells. The aim is to reduce the performance change of vibration reduction. Specifically, a diatomic lumped-mass model has been used, where one mass coefficient in each unit cell is subject to random error. The forced response is computed, and the frequency-averaged spatially maximum amplitude is used as the indicator to quantify the influence of the disorder. Then, we reveal the importance of the deviation at different unit cells by a global sensitivity analysis. A variance-based approach termed Sobol’s sensitivity analysis is used. The results show that the deviation in the unit cell nearest to the excitation source is of the greatest importance. A theoretical interpretation from the perspective of wave propagation is given. Eventually, a simple sorting strategy is proposed, and the rule is to ensure that the unit cell in the first position has the smallest deviation. This strategy can significantly improve the similarity of the dynamic characteristics between the nominal and disordered structures. Overall, the conducted work provides a reference to the manufacture and assembly of periodic structures and a further understanding of the vibration reduction in band gaps.