多层圆柱形波导中波特性的极坐标系全局离散化半解析公式

IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Jun Cao , Songhan Zhang , Miao Zhang , Chenguang Fan
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引用次数: 0

摘要

超声导波广泛应用于细长结构的健康监测。与著名的半解析有限元法(SAFE)不同,全局离散化半解析公式(GDSA)可以精确地满足所有连续性条件和边界条件,同时提高了计算效率,但目前只适用于笛卡尔坐标系下描述的板状问题,不适用于圆柱形波导。因此,在本研究中,极坐标系被引入到 GDSA 公式中,以在不损失精度的情况下提高计算多层圆柱波导中色散关系的计算效率。单元层的特征方程是根据虚功原理推导出来的。所涉及的矩阵以 Kronecker 积的形式明确推导,以减少待求值矩阵的维数,并引入了一个缩小的布尔矩阵,以避免中心点微不足道的径向位移引起的奇异性问题。首先分析了钢丝的频散曲线,并与根据波赫海默-克里方程求得的解析解进行了对比验证。以表面腐蚀的钢丝为两层为例,根据二次特征值方程求得频散曲线。结果发现,F(1,2) 模式的截止频率对腐蚀很敏感,具有探测隐藏电缆线腐蚀的潜力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A global-discretized semi-analytical formulation in polar coordinate system for the wave characteristics in multi-layer cylindrical waveguides

Ultrasonic guided waves are widely applied in health monitoring of slender structures. Being different from the well-known semi-analytical finite element method (SAFE), the global-discretized semi-analytical formulation (GDSA) exactly satisfies all the continuity and boundary conditions accurately while has improved computational efficiency, but is only applicable to the plate-like problems described in the Cartesian coordinate system currently, which is not applicable to the cylindrical waveguide. In the present work, the polar coordinate system is therefore introduced into the GDSA formulation to improve the computational efficiency of calculating the dispersion relation in a multi-layer cylindrical waveguide without loss of accuracy. The characteristic equations of the unit layer are derived from the principle of virtual work. The involved matrices are explicitly derived in the form of Kronecker product to reduce the dimension of the matrices to be evaluated and a reduced Boolean matrix is introduced to avoid the singularity problem caused by the trivial radial displacement of the central point. The dispersion curves of a steel wire are firstly analyzed and are verified in comparison with the analytical solutions solved from the Pochhammer-Chree equations. Taking the steel wire having a surface corrosion as a two-layer case example, the dispersion curves are obtained based on the quadratic eigenvalue equation. It is found that the cut-off frequency of the F(1,2) mode is sensitive to corrosion, having potential to detect corrosion of hidden cable wires.

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来源期刊
Computers & Structures
Computers & Structures 工程技术-工程:土木
CiteScore
8.80
自引率
6.40%
发文量
122
审稿时长
33 days
期刊介绍: Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.
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