Ultra-wide low-frequency bandgap design of acoustic metamaterial via multi-material topology optimization

Designing ultra-wide low-frequency bandgap acoustic metamaterial has important application potential but is also challenging. This study proposes a systematic topology optimization method of multi-material acoustic metamaterial to open single and multiple low-frequency bandgaps. In the optimization model, new objective functions that effectively evaluate the single or multiple low-frequency bandgaps are proposed. To describe the complicated topologies of the multi-material acoustic metamaterial with a lower number of design variables, the material-field series expansion (MFSE) technique is adopted, and the multiple material properties are interpolated with the discrete material optimization (DMO) scheme. With the interpolated scheme and the multi-material field description model, a clear three-material topology can be determined by two independent material-field functions with only 100 independent design variables. This greatly reduces the design variables for the topological description of the microstructure, enabling the problem to be solved using non-gradient optimization algorithms. The self-adaptive strategy based sequential Kriging optimization algorithm is then introduced to solve the optimization problems. Numerical examples prove the proposed topology optimization method can effectively provide the acoustic metamaterial designs with ultra-wide low-frequency bandgaps and show that both the Bragg scattering and local resonance mechanisms based acoustic metamaterial can be obtained directly without any additional settings.