In this paper, a computational methodology for the band structure analysis of 2D acoustic phononic structures based on the isogeometric boundary element method(IGABEM) is studied. IGABEM not only improves the accuracy of numerical model, but also retains the geometric accuracy and makes the pre-processing procedure relatively simpler for models designed through using computer-aided design(CAD) softwares. B-splines, which are widely employed in computer graphics and CAD industry, are used as basis functions for 2D phononic unit cells. The Bloch periodic boundary condition is directly specified to the control points on the virtual boundary of a unit cell. The Bloch eigenvalue problems derived with IGABEM show strong nonlinear features resulted from the adoption of fundamental solutions. To overcome the nonlinearity, a contour integral projection method with Gerschgorin disk theory-based eigenspace identification is introduced to the extraction of the Bloch eigenvalues for the description of dispersion curves. Numerical examples with models from different CAD softwares are investigated to demonstrate the accuracy and effectiveness of the proposed method.

本文研究了基于等几何边界元法（IGABEM）的二维声子声子结构能带结构分析的计算方法。IGABEM不仅提高了数值模型的准确性，而且保留了几何精度，并使使用计算机辅助设计（CAD）软件设计的模型的预处理程序相对简单。B样条曲线已广泛用于计算机图形学和CAD行业，被用作2D声子单元的基本功能。Bloch周期性边界条件直接指定给单位像元的虚拟边界上的控制点。IGABEM推导的Bloch特征值问题显示出由于采用基本解而产生的强大非线性特征。为了克服非线性，在基于Bloch特征值的提取中引入了基于Gerschgorin圆盘理论的特征空间识别的轮廓积分投影方法，以描述色散曲线。研究了来自不同CAD软件的模型的数值示例，以证明所提方法的准确性和有效性。