Mechanism and optimization study of bandgap regulation in three-component hexagonal lattice phononic crystals

To investigate how to achieve broader bandgaps within the mid-to-low frequency spectrum, this paper first designs a three-component hexagonal lattice phononic crystal structure and uses the FEM approach to analyze its band characteristics and transmission attenuation. Next, multiple vibration modes of this structure are analyzed, and the respective equivalent model is constructed. The calculation error between the equivalent model and the FEM approach is also analyzed. Finally, grounded in the equivalent model, the impact of different structural parameters on the bandgap is studied, and the structure is refined through Response Surface Methodology and the NSGA-II optimization algorithm. The results show that the three-component hexagonal lattice phononic crystal configuration has a complete bandgap within the frequency spectrum of 358.98–899.69 Hz. The calculation error between the equivalent model and the FEM approach is small, verifying the accuracy of the equivalent model. The lower bandgap boundary is primarily influenced by the scatterer’s mass, while the upper boundary is determined by the mass of the matrix. Compared to the original structure, the optimized hexagonal lattice phononic crystal has an increased bandgap width of 85.4 Hz. This paper provides valuable guidance for designing phononic crystals with specific bandgaps.