Modeling of wave dispersion along cylindrical structures using the spectral method.
Modeling of wave dispersion along cylindrical structures using the spectral method.
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DOI：
10.1121/1.2940577
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发表时间：
2008-08
期刊：
影响因子：
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通讯作者：
F. Karpfinger;B. Gurevich;A. Bakulin
中科院分区：
文献类型：
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作者：
F. Karpfinger;B. Gurevich;A. Bakulin
提出了一种求解由任意数量的弹性层和流体层组成的圆柱形分层介质的色散方程的算法和程序。该算法是基于谱方法，离散的基本波动方程的帮助下，谱微分矩阵和解决相应的方程作为一个广义特征值问题。对于给定的频率，本征值对应于不同模式的波数。这种技术的优点是易于实现，特别是对于传统的寻根方法受到很大限制或难以实现的情况，即，用于衰减、各向异性和多孔弹性介质。新方法的应用说明使用模型的弹性圆柱体和流体填充管。由此产生的色散曲线与分析结果吻合良好，这证实了该方法的准确性。本文计算了一系列频率下自由圆柱体中基模的粒子位移分布。
Algorithm and code are presented that solve dispersion equations for cylindrically layered media consisting of an arbitrary number of elastic and fluid layers. The algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wave numbers of different modes. The advantage of this technique is that it is easy to implement, especially for cases where traditional root-finding methods are strongly limited or hard to realize, i.e., for attenuative, anisotropic, and poroelastic media. The application of the new approach is illustrated using models of an elastic cylinder and a fluid-filled tube. The dispersion curves so produced are in good agreement with analytical results, which confirms the accuracy of the method. Particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies.