Predicting wave attenuation in sonic crystals using complex band structures calculated by boundary DOF replacement Bloch Mode Synthesis (BDR-BMS) for Unfitted Boundary Meshes

Abstract

Designing a sonic crystal acoustic barrier requires understanding the crystal's acoustic attenuation, which can be predicted using its complex band structure. This paper presents an efficient Boundary DOF Replacement Bloch Mode Synthesis (BDR-BMS) method, which focuses on the challenge of unfitted boundary meshes within the framework of the finite element method to calculate the complex band structure. The method introduces pairwise fitted boundary DOFs and establishes a linear relationship between unfitted and fitted boundary DOFs, which can also facilitate reduction of boundary DOFs. Combined with the BMS method, the BDR-BMS method achieves higher numerical efficiency compared to the conventional extended BMS method. Utilizing the computed complex band structure, a wave profile decomposition (WPD) method is presented to quantitatively predict wave attenuation behaviors. Results show that wave attenuation depends on the acoustic source profile, eigen wavenumbers derived from the band structure, and the decomposition of boundary profiles from different Bloch wave modes. Also, the wave attenuation behavior is due to the excitation of evanescent Bloch wave modes. With this knowledge, significant wave attenuation can be achieved in low frequency by exciting evanescent Bloch wave modes. Experiments are performed to verify our analyses.