Topological design of phononic band gap crystals with sixfold symmetric hexagonal lattice

Phononic band gap crystals offer great flexibility for manipulating elastic waves and can be used for many applications. The occurrence of band gaps highly depends on the spatial distribution of material phases in phononic crystals. This paper investigates topology optimization of two-dimensional (2D) solid/solid hexagonal-latticed phononic crystals with sixfold symmetry for maximizing specified band gaps. The optimization algorithm based on the bi-directional evolutionary structural optimization (BESO) method is established and verified by numerical examples. Various novel patterns with large band gaps for out-of-plane and in-plane waves are obtained and optimized solutions are discussed and compared with those of square-latticed ones. Based on the optimized solutions for out-of-plane waves and in-plane waves, the proposed method is extended to the design of the complete band gaps. The transmission analysis of the finite phononic structure formed by optimized phononic crystals shows that out-of-plane waves and in-plane waves can be transmitted or prohibited, which agrees well with the obtained band gaps in optimization. The further improvement of the proposed BESO method is also recommended.