Topology optimization of two-dimensional magnetorheological elastomer phononic crystal plate with tunable bandgap considering a specified target frequency

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.