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Investigation of finite/infinite unidirectional elastic phononic plates by BEM

机译：用有限元法研究有限/无限单向弹性声子板

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The investigation of finite/infinite unidirectional elastic phononic plates is carried out by using the boundary element method (BEM). The transmissions of elastic waves in finite structures are calculated by solving a size-reduced system matrix, in which the transfer matrix formulated by BEM is used repeatedly and the unknown quantities on the free boundaries of cells are removed. For the infinite structures, the Bloch theorem is applied to the unit cell that has traction free boundaries, and the dispersion relation is plotted by extracting the eigenfrequencies of the nonlinear Bloch eigenvalue problem using a contour integral method. Furthermore, the eigenfrequencies of the finite structure are extracted by applying the contour integral method to the sized reduced system matrix, and a banded distribution of the eigenfrequencies is found. The correlation between the band structures of the infinite structures and the elastic wave transmission of the corresponding finite structures are presented. The frequency-banded nature exhibited by the finite structures shows a good agreement with the band structure of the corresponding infinite structures.
机译：利用边界元法（BEM）进行了有限/无限单向弹性声子板的研究。通过求解尺寸减小的系统矩阵来计算弹性波在有限结构中的透射率，该系统矩阵可重复使用由BEM公式化的传递矩阵，并消除了细胞自由边界上的未知量。对于无限结构，将Bloch定理应用于具有无牵引力边界的晶胞，并使用轮廓积分法通过提取非线性Bloch特征值问题的特征频率来绘制色散关系。此外，通过将轮廓积分方法应用于尺寸减小的系统矩阵，提取有限结构的本征频率，并找到本征频率的带状分布。给出了无限结构的能带结构与相应有限结构的弹性波传输之间的相关性。有限结构所表现出的频带特性与相应无限结构的能带结构具有良好的一致性。

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