Calculation method and topology optimization design of phononic crystal considering discrepancies from ideal 2D models

There are obvious differences in band structures between thin-plate phononic crystals (PnCs) and ideal two-dimensional PnCs, which significantly affects the accuracy of band gap (BG) prediction and further restricts the topological optimization performance of plate-type PnC structures. To solve this problem, this study systematically derives the band structure calculation methods of PnCs under plane stress and plane strain assumptions, and mainly establishes the calculation model for flexural wave BGs of PnC plates based on Mindlin moderately thick plate theory. Band structure calculations and comparisons of typical structures verify the effectiveness of the proposed method, and the applicability of Mindlin plate theory to BG calculation of PnC plates is clarified. A BG optimization framework based on the floating projection topology optimization is constructed to drive optimized configurations toward clear 0/1 binary distribution. This framework is employed to perform multi-mode and multi-order band gap optimization of two-phase PnCs under various theoretical models. The influences of BG order and plate thickness on the optimized width of flexural wave BGs are discussed. Typical optimized results are selected for experimental tests to validate the accuracy of the proposed calculation and optimization methods.