A semi-analytical wavelet finite element method for wave propagation in rectangular rods

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-03-20 DOI:10.1016/j.wavemoti.2024.103325

Wenxiang Ding, Liangtian Li, Hongmei Zhong, Ying Li, Danyang Bao, Sheng Wei, Wenbin Wang

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Abstract

Prior knowledge of the dispersion curves and mode shapes of guided waves provides valuable information for wave mode selection and excitation in the field of non-destructive evaluation (NDE) and structural health monitoring (SHM). They are typically computed by the matrix methods, the finite element (FE) and semi-analytical finite element (SAFE) methods. However, the former is prone to numerical instability, and the latter two are limited by the refinement level of the FE mesh. In this paper, a semi-analytical wavelet finite element (SAWFE) method is presented to characterize wave propagation in rectangular rods. The piecewise polynomial interpolation functions of the SAFE method are replaced by two-dimensional scaling functions of the B-spline wavelet on the interval (BSWI). To demonstrate the accuracy of the proposed SAWFE technique, the propagation of guided waves in an aluminium plate is studied first. Then, the propagation of guided waves in rectangular rods of arbitrary aspect ratio is investigated. The results of this work clearly show that the SAWFE method presented here has higher accuracy and efficiency than the SAFE method.

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矩形杆中波传播的半解析小波有限元方法

导波的频散曲线和模态振型的先验知识为无损评估（NDE）和结构健康监测（SHM）领域的波模选择和激励提供了宝贵的信息。它们通常由矩阵方法、有限元（FE）和半解析有限元（SAFE）方法计算得出。然而，前者容易出现数值不稳定性，而后两者则受到有限元网格细化程度的限制。本文提出了一种半解析小波有限元（SAWFE）方法，用于描述矩形棒中波的传播特性。SAFE 方法中的分片多项式插值函数被区间 B 样条小波 (BSWI) 的二维缩放函数所取代。为了证明所提出的 SAWFE 技术的准确性，首先研究了导波在铝板中的传播。然后，研究了导波在任意长宽比矩形棒中的传播。研究结果清楚地表明，本文提出的 SAWFE 方法比 SAFE 方法具有更高的精度和效率。

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来源期刊

Wave Motion 物理-力学

CiteScore

4.10

自引率

8.30%

发文量

118

审稿时长

3 months

期刊介绍： Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.