Bandgap estimation and broadening of piezoelectric metamaterial beams undergoing longitudinal vibration

In the realm of acoustic metamaterials, two crucial challenges have attracted significant interests: (1) How to predict the bandgap range fast and accurately? (2) How to achieve a broader bandgap at a relatively low cost? This paper addresses these challenges by analyzing a type of piezoelectric (PZT) metamaterial beams comprising unit cells with sub-cells undergoing longitudinal vibration. The longitudinal bandgap estimation relationship based on the effective medium theory is proposed for the first time to estimate the bandgap range of PZT metamaterial beams with unit cells containing sub-cells, and verified with the transfer matrix method. Moreover, novel methods are introduced to construct graded PZT metamaterial beams by combining different sub-cells within a single cell. The proposed graded PZT metamaterial beams occupy significantly less space than conventional graded counterparts and exhibit wider longitudinal bandgaps compared to uniform PZT metamaterial beams.