PWAS激励Lamb波的谱有限元建模及参数研究

基于谱有限元法发展了一种由压电晶片主动传感器(PWAS)、胶层和主结构组成的三层模型,来模拟PWAS激励结构中Lamb波的传播。首先在各层使用不同的梁理论,推导PWAS-胶层-主结构三层模型的控制方程和力的边界条件,建立谱有限元模型。通过和传统的有限单元法进行比较,表明了在显著提高计算效率的同时,所发展谱有限元模型在分析结构中Lamb波传播上仍具有较高的精度。分析了激励频率、PWAS长度与厚度、胶层厚度等参数变化对输出电压信号的影响,可以为基于PWAS和Lamb波的主动健康监测技术提供参考。     

基于SBFEM和深度学习的裂纹状缺陷反演模型

结构内部缺陷的识别是结构健康监测的重要研究内容, 而当前以无损检测为主的结构安全检测多以定性分析为主, 定量识别缺陷的尺度较困难. 本文将比例边界有限元法(scaled boundary finite element methods, SBFEM)和深度学习相结合, 提出了基于Lamb波在结构中传播时的反馈信号定量识别结构内部裂纹状缺陷的反演模型. 通过随机生成缺陷信息(位置、大小), 采用SBFEM模拟Lamb波在含不同缺陷信息的结构中的信号传播过程, SBFEM仅需对结构边界离散可最小化网格重划分过程, 大大提高了计算效率. Lamb波在含裂纹状缺陷结构中传播时观测点的反馈信号包含大量的裂纹信息, 基于这一特性可为深度学习模型提供足够多的反映问题特性的训练数据. 建议的缺陷反演模型规避了传统反分析问题的目标函数极小化迭代过程, 在保证计算精度的前提下大大减少了计算成本. 对含单裂纹和多裂纹板的数值算例进行分析, 结果表明: 建立的缺陷识别模型能够准确地量化结构内部的缺陷, 对浅表裂纹亦有很好的识别效果, 且对于含噪信号模型仍具有较好的鲁棒性.      

基于电磁声激励Lamb波的裂纹深度检测

本文采用电磁声传感器接收单一S₀模态激励，测量Lamb波在板中不同深度的槽形裂纹处的反射与透射，用于对已知扩展长度的表面裂纹进行深度测量。然后分析了Lamb波模态的频散与波动特性，由超声Lamb波的波结构，近似计算了S₀模态入射到裂纹时的反射系数。计算结果与实验结果一致。结果表明，Lamb波在有限长裂纹处的反射系数可采用二维模型中的反射系数求解公式近似求解。采用电磁超声传感器接收单一S₀模态激励，重复测量稳定性高，适用于Lamb波反射系数的测量。Lamb波的反射系数与裂纹深度有很好的对应关系，可用于板表面已知长度裂纹的深度测量。     

Nondestructive testing method based on lamb waves for localization and extent of damage

Based on Lamb wave analysis of propagation in plate-like structures, a damage detection method is proposed that not only locates the position of the damage accurately but also estimates its size. Similar damage detection methods focus only on localization giving no quantitative estimation of extent. To improve detection, we propose two predictive circle methods for size estimation. Numerical simulations and experiments were performed for an aluminum plate with a hole. Two PZT configurations of different sizes were designed to excite and detect Lamb waves. From cross-correlation analysis, the damage location and extent can be determined. Results show that the proposed method enables a better quantitative resolution in detection, the size of the inspection area influences the accuracy of damage identification, and the closer is the inspected area to the damage, the more accurate are the results. The method proposed can be developed into a multiple-step detection method for multi-scale analysis with prospective accuracy.     

板状结构自发大变形问题的三维数值分析

花朵、树叶等自然界的板状结构因发生大变形而具有婀娜多姿的形状, 工程实际的板状结构也会出现类似现象. 板状结构是指完全相同的面状结构在厚度方向堆砌而形成的厚度尺寸比面内尺寸相比较小的一类特殊三维结构, 在生长或外部环境等因素产生的不协调变形激励下, 这类结构会形成内部应力, 本文研究因之而发生的自发大变形行为. 首先, 将板状结构的变形能分离为类伸缩变形能和剩余变形能两部分, 并提出基于三维大变形有限元分析的能量计算方法; 然后, 建立板状结构的屈曲失稳条件为剩余变形能由小到超越类伸缩变形能的跨越点, 进而提出转变厚度概念, 通过与简支方板失稳的经典理论解比较, 验证三维大变形有限元分析结果及屈曲失稳条件; 最后, 运用三维大变形有限元方法, 研究几种典型自发大变形问题, 分析不协调变形因素对内部应力场拉压特性和模式转变厚度的影响规律. 本文工作表明, 板状结构的大变形过程是弹性变形能中剩余变形能从零开始增加、直至超过类伸缩变形能引起屈曲的一个自发现象. 特别地, 三维大变形有限元分析是求解复杂内部应力场激发的板状结构屈曲失稳问题的一条有效途径.      

Lamb wave mode decomposition using concentric ring and circular piezoelectric transducers

Lamb waves using surface-bonded piezoelectric transducers (PZTs) have been widely used for nondestructive testing (NDT). However, the identification of individual Lamb wave modes and the subsequent data interpretation are often difficult due to the dispersive and multimodal natures of Lamb waves. To tackle the problem, a Lamb wave mode decomposition technique using concentric ring and circular PZTs is proposed. Its advantages over the conventional approaches are that (1) PZTs need to be placed only a single surface of a specimen and (2) mode decomposition can be performed at any desired frequency without changing the PZT size and/or spacing configuration. The proposed mode decomposition technique is formulated by solving 3D Lamb wave propagation equations considering the PZT size and shape, and this technique requires a specially designed dual PZT composed of concentric ring and circular PZTs. The effectiveness of the proposed technique for the Lamb wave mode decomposition is investigated through numerical simulation and experimental tests performed on an aluminum plate.     

基于Mindlin板理论的偏移损伤成像数值仿真研究

提出了一种应用散射Lamb波的偏移技术对板结构中多部位损伤进行实时识别.基于Mindlin板理论,推导了板结构中弥散性弯曲波频率-波数域的快速偏移方法.首先对由线性传感器阵列激励和接收到的入射和散射波场在波数-频率域分别进行延拓,然后根据Huygens原理,结合波场延拓的时间一致性原理施加成像条件,对损伤进行成像识别.数值仿真研究采用基于Mindlin板理论的有限差分法模拟结构中含不同形状及尺寸损伤时的散射波场.对模拟散射波场进行偏移成像的结果表明该方法不仅能够识别多部位损伤的位置,还具有识别损伤程度的能力,其快速计算的优点满足在线结构健康监测系统对实时性的要求.     

Lamb波在复合材料板中传播的谱有限元模拟

众所周知Lamb波在复合材料中的传播呈各向异性的特点,经典有限元法模拟这类问题效率不高,所以,本文采用谱有限元法进行研究。先建立了一种新的谱有限板单元,该单元以Gauss-Lobatto-Legendre点作为节点,使质量矩阵是对角矩阵;另外,该单元采用了扩展的位移场,能够较好地模拟板结构的三维特性。然后,对复合材料板结构中Lamb波在对称模式与反对称模式下的传播速度进行了求解,将计算结果与Mindlin板谱单元的结果以及三维弹性理论的结果进行了比较,并讨论了Lamb波在反对称层合板中的传播特点。最后,模拟了Lamb波在含和不含损伤复合材料层合板中的传播,数值结果表明所建立的谱有限板单元可以较好地模拟出Lamb波在复合材料板结构中的传播特性。     

Response of second-harmonic generation of Lamb wave propagation to microdamage thickness in a solid plate

The response features of second-harmonic generation (SHG) of primary Lamb wave propagation to the thickness of microdamage layer (MDL) in a solid plate have been theoretically and numerically investigated in this paper. Here the solid plate with a MDL is regarded as a double-layered plate in analysis of nonlinear Lamb wave propagation. On the basis of a second-order perturbation approximation and modal expansion analysis, the physical process of cumulative SHG by primary Lamb wave propagation in a solid plate with a MDL has been investigated. The influence of variation in the thickness of MDL on the effect of SHG of primary ${\mathit{S}}_0$ mode, which satisfies an approximate phase velocity matching in the low frequency region, has been theoretically analyzed, and then the finite element (FE) simulation has been carried out to validate the results of the theoretical predictions. A close agreement between the theoretical analyses and FE simulations validates the effectiveness of using the effect of SHG of primary ${\mathit{S}}_0$ mode for characterizing changes in the thickness of MDL. Moreover, change mechanism of nonlinear acoustic parameter with the thickness of MDL is revealed It is expected that the results obtained can provide a convenient means for accurately characterizing nonhomogeneous microdamage (MDL thickness) in layered plates.     

Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides

In this paper, a novel wavelet based spectral finite element is developed for studying elastic wave propagation in 1-D connected waveguides. First the partial differential wave equation is converted to simultaneous ordinary differential equations (ODEs) using Daubechies wavelet approximation in time. These ODEs are then solved using finite element (FE) technique by deriving the exact interpolating function in the transformed domain. Spectral element captures the exact mass distribution and thus the system size required is very much smaller then conventional FE. The localized nature of the compactly supported Daubechies wavelet allows easy imposition of initial-boundary values. This circumvents several disadvantages of the conventional spectral element formulation using Fast Fourier Transforms (FFT) particularly in the study of transient dynamics. The proposed method is used to study longitudinal and flexural wave propagation in rods, beams and frame structures. Numerical experiments are performed to show the advantages over FFT-based spectral element methods. The efficiency of the spectral formulation for impact force identification is also demonstrated.