各向异性材料弹性/声波导问题的谱元法
Spectral Element Method for the Elastic/Acoustic Waveguide Problem in Anisotropic Metamaterials
摘要：
为了模拟弹性波在非均匀介质复杂结构中的传播，常常需要得到弹性波导的传播本征模。由于假设波导在一个方向上是均匀的，通过在该方向上使用傅立叶变换，可以将原始的3-D问题转换为所谓的2.5-D问题。然而，弹性超材料（EMM）的引入拓宽了这一主题的视野，并要求在EMM波导的新功能，不能得到大多数传统的波导求解器。在这项工作中，谱元法（SEM）的发展，以模拟弹性/声波在各向异性介质中的各向异性的质量密度和/或负折射率参数的波导问题。据我们所知，扫描电镜还没有被引入以前这样的波导问题。对于具有各向异性密度的波导，在大多数商业软件包中不能用有限元法求解，我们设计了一个各向异性密度EMM波导与我们的SEM求解器，以展示一些有趣的现象。数值算例表明，谱元方法在精度和计算效率方面具有明显的优势，并与传统有限元方法进行了比较。
英文摘要：
In order to simulate elastic wave propagation in a complex structure with inhomogeneous media, we often need to obtain the propagating eigenmodes of an elastic waveguide. As the waveguide is assumed uniform in one direction, the original 3-D problem can be converted into a so-called 2.5-D problem by using the Fourier transform in that direction. However, the introduction of elastic metamaterials (EMM) broadens the horizon of this subject, and new features are required in EMM waveguides that cannot be obtained by most traditional waveguide solvers. In this work, a spectral element method (SEM) is developed to simulate the elastic/acoustic waveguide problem in anisotropic media with anisotropic mass density and/or negative index parameters. To the best of our knowledge, the SEM has not been introduced previously for such a waveguide problem. For waveguides with anisotropic density that cannot be solved by the FEM in most of commercial software packages, we design an anisotropic density EMM waveguide with our SEM solver to demonstrate some intriguing phenomena. The spectral element results are verified by several numerical examples through comparison with the traditional finite element method (FEM) to show its significant advantages in term of accuracy and computation efficiency.
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