Multi-objective optimized design of two-dimensional multi-phase phononic crystals with materials self-selection

Abstract

In this paper, the multi-objective optimization problem (MOOP) of selecting suitable materials from four materials for phononic crystals layouts is investigated based on an optimization method combined nondominated sorting-based genetic algorithm II (NSGA-II) and finite element method (FEM). Driven by different optimization objectives, the changes in the optimized structure compared to the seed structure are the change of the bandgap mechanism from a local resonance mechanism to a Bragg scattering mechanism, the change of the included materials from four to three, and the significant change in the location and extent of the pores and other materials, respectively. The obtained nondominated Pareto solution of MOOP can balance the bandgap and the structural mass, which provides the decision-maker trade-off to select the appropriate optimized solution. Compared with the single-objective optimization problem (SOOP), the MOOP not only obtains a nondominated solution close to the result of SOOP, but also obtains other nondominated solutions of MOOP, which proves the effectiveness of the optimization algorithm in this paper. The design method in this paper can be easily extended to select suitable materials from a wider variety of materials for bandgap optimization design of PnCs, which has very promising applications.