Fast band structure prediction for phononic crystals with double−stage model reduction and wave isogeometric analysis

Phononic crystals (PnCs), a well−known group of artificial metamaterials that demonstrate bandgap characteristics, are commonly utilized in multiple engineering fields. However, its design often faces the computational challenge of iterative band structure calculations, retarding the invention of new PnCs. In order to speed up the computation of band structures, this paper introduces a novel numerical method called double−stage reduced wave isogeometric analysis (DRWIGA). Isogeometric analysis is adopted to precisely describe the cell's geometry during modeling and analysis. The reduced−order model is obtained from a single cell undergoing a two−step reduction process: inner mode and boundary mode reduction. This significantly reduces the dimension of the problem, thereby expediting the calculation of band structures. The proposed method's efficiency and effectiveness are demonstrated by classic benchmark problems. This approach achieves a 94% decrease in model size for 2D PnCs, along with an impressive 99.7% reduction in CPU time for slowness surface calculations. It accelerates the bandgap optimization of PnCs and fosters novel metamaterial designs.