面内波倾斜传播的传递矩阵算法

Transfer Matrix Method for Oblique In-plane Waves Propagation

采用传递矩阵法研究压电效应的影响下面内波在一维压电声子晶体当中倾斜传播时的频散特性。传递矩阵法基本思想为:元胞中的子层、两侧状态向量可由关系矩阵相连,相邻子层的状态向量,由界面间的关系也可得到一联系矩阵,最后结合布洛赫(Bloch)定理,得到波在层状周期复合结构中传播的频散方程。主要研究对象为面内波,面内波是由P波和SV波耦合而成的,当面内波在周期结构中均匀传播时,P波和SV波同时在结构中传播。通过传递矩阵法得到面内波在一维层状周期结构当中倾斜传播时的频散方程,绘制相应带隙图,分析压电效应的影响。

The frequency dispersive characteristics of in-plane waves which propagate obliquely in one-dimensional piezoelectric phononic crystals are studied by transfer matrix method. The basic ideas of transfer matrix method are as follow： The cellular layer,the state vectors on both sides of a unit cell can be linked by a relationship matrix. By the relationship between interfaces,the state vectors of the adjacent sub-layers can also obtain a contact matrix. Then wave propagating dispersive equation in periodic layered composite structure is derived combined with Bloch theorem. The in-plane waves,which are coupled by P-wave and SV-wave,are the main objects of study. When in-plane waves travels uniformly in the periodic structure,P-wave and SV-wave travel in structure at the same time. Above all,the dispersive equation when in-plane waves propagating obliquely through piezoelectric phononic crystal is obtained by transfer matrix method,and then the diagrams of band gaps are completed. According to the equations and diagrams the effects of piezoelectric phase are analyzed.