Realization of full and directional band gap design by non-gradient topology optimization in acoustic metamaterials

Full and directional band gap acoustic metamaterials offer the promising ability of controlling and prohibiting propagation of acoustic/elastic waves in specified frequency ranges or directions. However, there is no guarantee that the optimization problem will be solved successfully with the existing gradient-based topology optimization methods because of the complexity of the problem and strong dependence on initial guesses. In this study, we developed a systematic topological optimization method based on material-field series expansion (MFSE) framework for full and directional band gap acoustic metamaterials design. Herein, the number of involved design variables of the MFSE method is greatly reduced to no more than 50, and an optimal band gap design of acoustic metamaterials is therefore able to be obtained with non-gradient optimization algorithms. Then, the Kriging-based optimization algorithm with a self-adaptive strategy is adopted for solving the optimization problem. The optimized designs finally converge to the orderly material distribution and numerical validations show improved full and directional propagation properties as expected. The realization of two dimension acoustic metamaterials demonstrates that the proposed method can generate meaningful optimized topologies of PnCs for the full frequency band and directional propagation with a broad frequency range. (C) 2020 Elsevier Ltd. All rights reserved.