The properties of optimal two-dimensional phononic crystals with different material contrasts

Abstract

By modifying the spatial distribution of constituent material phases, phononic crystals (PnCs) can be designed to exhibit band gaps within which sound and vibration cannot propagate. In this paper, the developed topology optimization method (TOM), based on genetic algorithms (GAs) and the finite element method (FEM), is proposed to design two-dimensional (2D) solid PnC structures composed of two contrasting elastic materials. The PnCs have the lowest order band gap that is the third band gap for the coupled mode, the first band gap for the shear mode or the XY34Z band gap for the mixed mode. Moreover, the effects of the ratios of contrasting material properties on the optimal layout of unit cells and the corresponding phononic band gaps (PBGs) are investigated. The results indicate that the topology of the optimal PnCs and corresponding band gaps varies with the change of material contrasts. The law can be used for the rapid design of desired PnC structures.