基于FFT的Bloch波分析方法：在多晶体中的应用
An FFT-based approach for Bloch wave analysis: application to polycrystals
摘要：
提出了一种基于快速傅里叶变换的方法，用于求解任意微结构非均匀周期介质中声波的频散关系。使用体素化的代表性体积元素（RVE）明确地考虑微观结构。在傅里叶空间中求解布洛赫波的本征值问题，得到了频散图。为此，通过在傅立叶空间中使用微分算子，定义了代表刚度和质量的两个线性算子。最小特征值的获得使用隐式重新启动Lanczos和子空间迭代方法，和所需的逆刚度算子是使用共轭梯度与预条件子。用该方法研究了弹性多晶体中声波的传播，表明晶体各向异性和多晶体织构对声波传播有很强的影响。结果表明，该方法结合了经典的傅立叶级数分析的简单性与有限元的多功能性，以考虑复杂的几何形状，证明了一种有效的和通用的方法，允许在3D中使用大型RVE。
英文摘要：
A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
