A level set-based topology optimization method for the design of finite phononic crystals

This study presents a level set-based topology optimization method for finite phononic crystals. To minimize the wave transmission on the boundary of the output domain, the adjoint method is employed to derive the topological derivatives. The boundary element method is then utilized to efficiently solve both the original and adjoint elastic dynamic problems, allowing for effective handling of boundary conditions. The boundaries of the material region are described by the zero-contour line of the level set function. Within a finite periodic unit, the optimization is performed, and numerical examples are provided for different frequency ranges. The results show that the proposed method can significantly reduce the wave transmission at a specific frequency and exhibit good vibration isolation performance. The vibration isolation effect can be increased by increasing the number of optimized layers, but the attenuation band gap is not necessarily enlarged. A parameter is also investigated for its influence on structural complexity, demonstrating that appropriate adjustment can balance geometric complexity and engineering feasibility. This method provides an effective means for the optimal design of phononic crystals and has the potential to be extended to a wider range of elastic metamaterial design problems.