Band structure analysis for 2D acoustic phononic structure using isogeometric boundary element method. (November 2020) - Gao, Haifeng; Chen, Leilei; Lian, Haojie; Zheng, Changjun; Xu, Huidong; Matsumoto, Toshiro
Highlights: Bloch eigenvalue problems in phononic structures are formulated using isogeometric boundary element method. Bloch boundary condition is directly specified to the control points of the boundary of unit cell. Nonlinear eigenvalue problems are solved using a contour integral projection method with Gerschgorin disk theory. Models designed by using both Computer-Aided Design software and graphic software are computed. Abstract: 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.