Multiobjective Optimization of Two-Dimensional Phononic Bandgap Materials and Structures Using Genetic Algorithms

In this paper, two-dimensional phononic bandgap materials are designed through multiobjective optimization using the genetic algorithm. Two cases are given. In Case I, 2D phononic crystals (PnCs) with maximum bandgap and minimum mass are optimized. The optimal results show that the third-order relative bandgaps become large, along with the increase in mass. In Case II, 2D local resonance phononic crystals (LRPnCs) simultaneously maximizing the third and sixth relative bandgap widths (RBWs) are designed. The frequency response function of the optimized structures shows that the attenuation of elastic waves is most remarkable at the beginning frequency of the bandgap. Finally, an integrated structure, which accumulates the bandgaps of three optimized substructures, is proposed. These results provide a new approach for bandgap design.