A rasterized plane wave expansion method for complex 2-D phononic crystals

Abstract

This paper introduces a computer image processing-based method called the rasterized plane wave expansion method (RPWEM). This method improves the conventional plane wave expansion method (CPWEM) and reduces its formula derivation cost in the case of 2-D phononic crystals with complex inclusions. In addition, for 2-D phononic crystals with arbitrary multiphase materials, this method can also simplify the calculation process. By employing the proposed RPWEM, successful calculations of band gaps are conducted for planar phononic crystals with the hexagonal unit cell as well as phononic crystals featuring integrated circuit-like structures. The results further validate the expanded applicability of the RPWEM in comparison to the CPWEM. In the end, a potential application similar to DIC (Digital Image Correlation) for predicting band structures of phononic crystals is proposed, and its feasibility is briefly validated.