Petrov–Galerkin method for the band structure computation of anisotropic and piezoelectric phononic crystals
Petrov–Galerkin method for the band structure computation of anisotropic and piezoelectric phononic crystals
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用于计算各向异性和压电声子晶体能带结构的 PetrovGalerkin 方法
DOI：
10.1016/j.apm.2020.08.026
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发表时间：
2021
影响因子：
5
通讯作者：
Songming Hou
中科院分区：
文献类型：
--
作者：
Liqun Wang;Hui Zheng;Meiling Zhao;Liwei Shi;Songming Hou
本文将Petrov-Galerkin有限元界面法改进为矢量形式，并应用于计算具有复杂散射体几何形状的声子晶体的能带结构。该方法采用值周期子空间和投影网格。完整的数学模型，连同连续性和平衡条件的散射体界面，以及布洛赫周期性的边界条件的单位细胞。然后应用该方法计算了三种特殊声子晶体的能带结构：含各向异性夹杂的声子晶体、含压电材料的声子晶体和含纳米压电材料的声子晶体。利用非对称基函数和非贴体网格的优点，我们的方法适用于具有复杂散射体几何形状的声子晶体的计算和分析。通过大量的数值试验，验证了该方法的精度和收敛性。研究了各向异性夹杂的旋转角、散射体的复杂形状、散射体的填充率以及散射体的旋转角对这三种声子晶体能带结构的影响。这将为设计和制备具有特定能带结构的声子晶体提供新的视角。
In this paper, the Petrov-Galerkin finite element interface method is modified to the vectorial form and applied to compute the band structure of phononic crystals with complicated scatterer geometry. Value-periodic subspace and projective grid are employed in this method. Complete mathematical model together with the continuity and equilibrium conditions on the scatterer interface as well as the Bloch-periodic boundary conditions on the unit cell are presented for these systems. We then apply this method to compute the band structure of three kinds of special phononic crystals: phononic crystal with anisotropic inclusions, phononic crystal containing piezoelectric materials and phononic crystal containing nano-piezoelectric materials. Taking advantage of asymmetric basis functions and non-body-fitted meshes, our method is suitable for the calculation and analysis of phononic crystals with complicated scatterer geometries. With plenty of numerical experiments, the accuracy and convergency of the proposed method is demonstrated. The influences of the rotation angle of anisotropic inclusion, complicated scatterer shape, filling fraction of the scatterers, and the rotation angle of the scatterers to the band structure of these three kinds of phononic crystals are investigated. This will provide a new perspective for the design and manufacture of phononic crystals with specific band structures.
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DOI：
10.1103/physreve.67.065602
发表时间：
2003-06
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
M. Wilm;A. Khelif;S. Ballandras;V. Laude;B. Djafari-Rouhani
通讯作者：
M. Wilm;A. Khelif;S. Ballandras;V. Laude;B. Djafari-Rouhani
DOI：
10.1016/j.jcp.2017.03.003
发表时间：
2016-07
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Hailong Guo;Xu Yang
通讯作者：
Hailong Guo;Xu Yang
布洛赫周期边界条件界面问题的Petrov-Galerkin有限元界面法及其在声子晶体中的应用
影响因子：
4.1
作者：
Wang Liqun;Zheng Hui;Lu Xin;Shi Liwei
通讯作者：
Shi Liwei
DOI：
10.36045/bbms/1337864268
发表时间：
2012-06
影响因子：
0.5
作者：
T. Geyikli;S. B. G. Karakoç
通讯作者：
T. Geyikli;S. B. G. Karakoç
影响因子：
1.7
作者：
Liqun Wang;Songming Hou;Liwei Shi
通讯作者：
Liqun Wang;Songming Hou;Liwei Shi