Modeling and Analysis of Ellipticity Dispersion Characteristics of Lamb Waves in Pre-stressed Plates

IF 2.6 3区材料科学 Q2 MATERIALS SCIENCE, CHARACTERIZATION & TESTING

Journal of Nondestructive Evaluation Pub Date : 2024-10-25 DOI:10.1007/s10921-024-01133-1

Yizheng Zhang, Yan Lyu, Jie Gao, Yang Zheng, Yongkang Wang, Bin Wu, Cunfu He

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Abstract

In this research, based on the weak nonlinear elasticity theory and finite deformation theory, a dynamic equation of guided waves in pre-stressed plates is established. Legendre orthogonal polynomials expansion method is employed to analytically solve wave equations. The dispersion curves and particle trajectory are obtained without root-finding algorithm. The solution is validated by comparing with the superposition of partial bulk wave method, and its convergence properties are analyzed. The effects of the pre-stress states on particle trajectory and ellipticity dispersion curves are investigated. Results confirm that the behavior of particle trajectory and ellipticity dispersion depends not only on the pre-stress states but also on frequency and mode. Next, ellipticity dispersion curve of fundamental Lamb modes with various stress state and propagation directions are calculated. Finally, the sensitivity of ellipticity as an indicator of stress is also analyzed. These results provide useful reference for the development of innovative nondestructive testing method for pre-stress states based on Lamb waves.

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预应力板中λ波的椭圆度频散特性建模与分析

本研究基于弱非线性弹性理论和有限变形理论，建立了预应力板中的导波动态方程。采用 Legendre 正交多项式展开法对波方程进行解析求解。在不使用寻根算法的情况下，得到了频散曲线和粒子轨迹。通过与部分体波叠加法进行比较，验证了求解结果，并分析了其收敛特性。研究了预应力状态对粒子轨迹和椭圆度频散曲线的影响。结果证实，粒子轨迹和椭圆度频散的行为不仅取决于预应力状态，还取决于频率和模式。接着，计算了不同应力状态和传播方向的基本 Lamb 模式的椭圆度频散曲线。最后，还分析了椭圆度作为应力指标的敏感性。这些结果为开发基于 Lamb 波的创新型预应力状态无损检测方法提供了有益的参考。

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

Journal of Nondestructive Evaluation 工程技术-材料科学：表征与测试

CiteScore

4.90

自引率

7.10%

发文量

审稿时长

9 months

期刊介绍： Journal of Nondestructive Evaluation provides a forum for the broad range of scientific and engineering activities involved in developing a quantitative nondestructive evaluation (NDE) capability. This interdisciplinary journal publishes papers on the development of new equipment, analyses, and approaches to nondestructive measurements.