A new perspective for analyzing complex band structures of phononic crystals

Rewriting the formulation of the Bloch waves, this paper presents a new perspective for analyzing the complex band structures of the in-plane waves in 2D phononic crystals. Using the proposed formulation, a new finite element based method is developed for analyzing 2D periodic systems. The results of the validation example prove that the proposed method can provide exact solutions for both the real and complex band structures of 2D periodic systems. Furthermore, using the proposed method, the complex band structures of a 2D periodic structure are calculated. The physical meanings of the obtained complex band structures are discussed by performing the wave mode analysis.