BESO approach to topology optimization of GaN phononic crystals

The use of Phononic Crystals (PnC) in suspended structures and microstructures, such as plates and slabs, has gained a lot of attention in the past years for the wide range of feasible applications (acoustic waveguides, acoustic insulation, acoustic cloaking) and for the easy fabrication technique. Since the performance of the device is related to the band of frequencies reflected by the PnC and since this band (called bandgap) depends on the geometric and material properties of the fundamental unit cell of the PnC, a useful tool for the design of those structures is topology optimization. This paper is focused on a novel and fast engineering use of Bidirectional Evolutionary Structural Optimization for the definition of the optimal hole configuration in air-solid PnC. The technique adopted finds the optimal shape of the hole in less than 20 iterations, and it is easy implemented in a 2D plane strain Matlab finite element solver.