Phononic crystals with tunable bandgap characteristics have attracted increasing research interest. In order to design the widest tunable bandgap, a magnetorheological elastomer phononic crystal plate (MREPCP) was developed and a topology optimization method based on the sequential Kriging-based material-field series expansion (KG-MFSE) method and the bi-material model was proposed for the MREPCP in this paper. The bandgap calculated by the improved plane wave expansion (IPWE) method is consistent with the simulated bandgap obtained by the finite element method (FEM) for the in-plane mode. Subsequently, three numerical examples of topology optimization considering different target frequencies are discussed. The bandgap and transmissibility results consistently verify the effectiveness of the KG-MFSE method in widening the bandgap as well as the tunability of the bandgap for the optimized MREPCP. Finally, the desired waveguides with different predefined paths have been implemented by applying magnetic fields without modifying the structure of the optimized MREPCP, demonstrating good potential for application.

具有可调谐带隙特性的声子晶体引起了越来越多的研究兴趣。为了设计最宽的可调谐带隙，开发了磁流变弹性体声子晶体板（MREPCP），并提出了基于顺序克里金材料场级数展开（KG-MFSE）方法和双材料模型的拓扑优化方法。本文提出了 MREPCP。改进的平面波展开（IPWE）方法计算的带隙与面内模式的有限元方法（FEM）模拟得到的带隙一致。随后，讨论了考虑不同目标频率的拓扑优化的三个数值示例。带隙和透射率结果一致验证了 KG-MFSE 方法在加宽带隙方面的有效性以及优化 MREPCP 的带隙可调性。最后，在不修改优化后的MREPCP结构的情况下，通过施加磁场实现了具有不同预定义路径的所需波导，展示了良好的应用潜力。