Edge resonance in discrete elastic waveguides and its convergence to isotropic continuous media

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science Pub Date : 2025-06-20 DOI:10.1016/j.ijengsci.2025.104307

G. Carta , M.J. Nieves , M. Brun , V. Pagneux

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Abstract

We discuss the problem of edge resonance for Lamb waves in a semi-infinite discrete elastic strip, represented by a triangular lattice. In analogy with the reflection problem in the corresponding continuum, for real frequencies the edge resonance phenomenon for the lattice strip is characterised by localised vibrations at its free edge. By characterising the reflection coefficient in the complex frequency plane, we then verify the existence of a complex edge resonance frequency for the lattice, associated with a mode of the homogeneous problem without incident wave. Importantly, when the number of rows in the strip of fixed width is large, we show that the lattice edge resonance frequency converges to the corresponding frequency in the analogous continuum problem for the effective strip. Interestingly, convergence to the complex edge resonance frequency is monotonic only with respect to its real part, while its imaginary part exhibits a minimum absolute value, numerically undistinguishable from zero, for a lattice strip with 65 rows in the transverse direction.

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离散弹性波导中的边缘共振及其在各向同性连续介质中的收敛性

讨论了用三角形晶格表示的半无限离散弹性条上Lamb波的边缘共振问题。与相应连续介质中的反射问题类似，对于实频率，晶格条的边缘共振现象的特征是其自由边缘的局部振动。通过表征复频率平面上的反射系数，我们验证了晶格的复边缘共振频率的存在性，该频率与无入射波的齐次问题的模态有关。重要的是，当固定宽度条带的行数较大时，我们证明了在有效条带的类似连续问题中，晶格边缘共振频率收敛于相应的频率。有趣的是，对复边缘共振频率的收敛只对其实部是单调的，而其虚部表现出最小绝对值，在数值上与零无法区分，对于横向有65行的晶格条。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Engineering Science 工程技术-工程：综合

CiteScore

11.80

自引率

16.70%

发文量

审稿时长

45 days

期刊介绍： The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.