Maximizing spatial decay of evanescent waves in phononic crystals by topology optimization

The propagation of evanescent waves inside phononic band gaps is important for the design of phononic crystals with desirable functionalities. This paper extends the bi-directional evolutionary structure optimization (BESO) method to the design of phononic crystals for maximizing spatial decay of evanescent waves. The optimization objective is to enlarge the minimum imaginary part of wave vectors at a specified frequency. The study is systematically conducted for both out-of-plane and in-plane waves at various frequencies. Numerical examples demonstrate that the proposed optimization algorithm is effective for designing phononic crystals with maximum spatial decay of evanescent waves. Various topological patterns of optimized phononic crystals are given. The results also show that the proposed optimization algorithm can successfully overcome difficulties in opening band gap at desirable frequencies, especially for the complete band gap and multiple band gaps.