Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map  

作　　者：Ni Zhen Feng-Lian Li Yue-Sheng Wang Chuan-Zeng Zhang 

机构地区：[1]Institute of Engineering Mechanics,Beijing Jiaotong University,100044 Beijing,China [2]Department of Civil Engineering,University of Siegen,Siegen,D-57068,Germany

出　　处：《Acta Mechanica Sinica》2012年第4期1143-1153,共11页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(51178037,10632020);the 973 State Key Development Program for Basic Research of China(2010CB732104)

摘　　要：In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.

关 键 词：Phononic crystal Band structure Cylindrical wave expansion Dirichlet-to-Neumann （DtN） map Bloch theorem 

分 类 号：O156.4[理学—数学] P333.9[理学—基础数学]