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首页> 外文期刊>Engineering analysis with boundary elements >Boundary element method for band gap calculations of two-dimensional solid phononic crystals
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Boundary element method for band gap calculations of two-dimensional solid phononic crystals

机译：二维固体声子晶体带隙计算的边界元方法

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摘要

A boundary element method (BEM) is developed to calculate the elastic band gaps of two-dimensional (2D) phononic crystals which are composed of square or triangular lattices of solid cylinders in a solid matrix. In a unit cell, the boundary integral equations of the matrix and the scatterer are derived, the former of which involves integrals over the boundary of the scatterer and the periodic boundary of the matrix, while the latter only involves the boundary of the scatterer. Constant boundary elements are adopted to discretize the boundary integral equations. Substituting the periodic boundary conditions and the interface conditions, a linear eigenvalue equation dependent on the Bloch wave vector is derived. Some numerical examples are illustrated to discuss the accuracy, efficiency, convergence and the computing speed of the presented method.
机译：提出了一种边界元方法（BEM），以计算二维（2D）声子晶体的弹性带隙，该声子晶体由固态矩阵中的圆柱体的正方形或三角形晶格组成。在单位单元中，导出矩阵和散射体的边界积分方程，其中前者涉及散射体边界和矩阵周期边界上的积分，而后者仅涉及散射体边界。采用常数边界元离散边界积分方程。代入周期性边界条件和界面条件，推导出依赖于Bloch波矢的线性特征值方程。数值算例说明了该方法的准确性，效率，收敛性和计算速度。

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