受载结构中SH<sub>0</sub>波与裂纹作用的非线性散射场的数值研究

陈荟键; 朱清锋; 苗鸿臣; 冯志强

doi:10.21656/1000-0887.440029

受载结构中SH₀波与裂纹作用的非线性散射场的数值研究

doi: 10.21656/1000-0887.440029

西南交通大学力学与航空航天学院，成都 611756

基金项目:

国家自然科学基金项目 12172310

四川省自然科学基金项目 2022NSFSC0435

中国科协青年人才托举工程项目 YESS20210342

详细信息

作者简介:
陈荟键(1991—)，男，博士生(E-mail: huijianc@foxmail.com)

通讯作者:
冯志强(1963—)，男，教授，博士生导师(通讯作者. E-mail: zhiqiang.feng@univ-evry.fr)

我刊编委冯志强来稿
中图分类号: O343.3
计量
- 文章访问数: 471
- HTML全文浏览量: 191
- PDF下载量: 132
- 被引次数: 0
出版历程
- 收稿日期: 2023-02-02
- 修回日期: 2023-03-01
- 刊出日期: 2023-04-01

Numerical Study of Nonlinear Scattering Characteristics of SH₀ Waves Encountering Cracks in Prestressed Plates

School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 611756, P.R.China

Contributed by FENG Zhiqiang, M. AMM Editorial Board

摘要

摘要: 超声导波因具有传播距离远、能量衰减小等优点在结构健康监测领域中被广泛关注. 厘清结构中导波与损伤作用后的散射规律，对于传感器阵列的设计和信号分析均具有重要意义. 通过发展的数值方法，研究了受载结构中零阶水平剪切波(SH₀波)与微裂纹作用的接触声非线性作用规律. 在双势谱方法的基础上，进一步通过mortar方法将谱单元和有限单元进行了耦合，以充分利用谱元法计算导波传播效率高的优点和有限元在离散复杂结构中的优势. 利用该方法计算了板壳结构在自由状态和受载状态下SH₀波与不同角度微裂纹作用的非线性散射场. 结果表明，SH₀波与裂纹作用后的二次谐波散射场关于裂纹面近似对称分布，并且单轴预应力不会改变二次谐波散射场的对称性，仍可以通过散射场的分布来确定微裂纹的取向.
- 水平剪切波 /
- 接触声非线性 /
- 谱元法 /
- 双势接触理论
Abstract: Ultrasonic guided waves are widely used in structural health monitoring (SHM) for their long propagation distances and small energy attenuation. Understanding the scattering characteristics of guided waves encountering defects is essential for the design of transducer arrays and wave signal interpretation in SHM. The contact nonlinear scattering characteristics of the SH₀ wave (zero-order shear horizontal wave) encountering cracks in prestressed plates were investigated. Based on the previously developed bi-potential spectral method, the spectral finite elements (SFEs) and the finite elements (FEs) were further coupled with the mortar method to make full use of the high efficiency of the spectral element method in calculating guided wave propagation and the strong ability of the finite element method in discretizing complex structures. The nonlinear scattering fields of SH₀ waves interacting with microcracks at different angles in plates under free and loaded conditions were calculated with the developed numerical method. The results show that, the induced 2nd harmonic scattering field is approximately symmetrical with respect to the crack direction. Moreover, the existence of uniaxial prestress will not change the symmetry of the 2nd harmonic scattering field, so the orientation of the microcrack can still be determined by the distribution of the scattering field.
- shear horizontal wave /
- contact acoustic nonlinearity /
- spectral element method /
- bi-potential contact theory
Contributed by FENG Zhiqiang, M. AMM Editorial Board
注释:

1) 我刊编委冯志强来稿

HTML全文

图 1 有限元和谱单元耦合示意图

Figure 1. Schematic diagram of the coupling of finite elements and spectral elements

下载: 全尺寸图片幻灯片

图 2 Coulomb摩擦锥示意图

Figure 2. Schematic diagram of Coulomb's frictional cone

下载: 全尺寸图片幻灯片

图 3 SH₀波与微裂纹作用的非线性散射场计算模型

Figure 3. The calculation model for the nonlinear scattering characteristics of the SH₀ wave encountering cracks in prestressed plates

下载: 全尺寸图片幻灯片

图 4 不同角度裂纹建模原理图

Figure 4. Schematic diagram of the crack modeling at different angles

下载: 全尺寸图片幻灯片

图 5 不同时刻的非线性散射总位移云图

Figure 5. The nonlinear scattering fields at different moments

下载: 全尺寸图片幻灯片

图 6 无损伤和含微裂纹损伤工况下，时域信号和对应频谱图的比较

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 6. Comparison of time domain signals and corresponding frequency spectrums between the pristine case and the microcrack damaged case

下载: 全尺寸图片幻灯片

图 7 不同微裂纹取向对应的切向位移二次谐波归一化散射场

Figure 7. Normalized scattering fields of the 2nd harmonics for different microcrack orientations

下载: 全尺寸图片幻灯片

图 8 单轴拉伸状态下不同微裂纹取向时的切向位移二次谐波归一化散射场

Figure 8. Normalized scattering fields of the 2nd harmonics under uniaxial tension for different microcrack orientations

下载: 全尺寸图片幻灯片

图 9 主瓣方向的二次谐波幅值与拉应力的关系曲线

Figure 9. Relationships between the 2nd harmonic amplitude and the tensile stress in the direction of the main lobe

下载: 全尺寸图片幻灯片

图 10 单轴压缩状态下不同微裂纹取向对应的切向位移二次谐波归一化散射场

Figure 10. Normalized scattering fields of the 2nd harmonics under uniaxial compression for different microcrack orientations

下载: 全尺寸图片幻灯片

图 11 主瓣方向的二次谐波幅值与压应力的关系曲线

Figure 11. Relationships between the 2nd harmonic amplitude and the compressive stress in the direction of the main lobe

下载: 全尺寸图片幻灯片

参考文献(30)

[1]	SU Z Q, YE L. Identification of Damage Using Lamb Waves: From Fundamentals to Applications[M]. Berlin: Spring Science & Business Media, 2009.
[2]	刘瑶璐, 胡宁, 邓明晰, 等. 板壳结构中的非线性兰姆波[J]. 力学进展, 2017, 47: 201714. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201700014.htm LIU Yaolu, HU Ning, DENG Mingxi, et al. Nonlinear Lamb waves in plate/shell structures[J]. Advances in Mechanics, 2017, 47: 201714. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201700014.htm
[3]	孙迪, 朱武军, 项延训, 等. 微裂纹的非线性超声检测研究进展[J]. 科学通报, 2022, 67(7): 597-609. https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB202207003.htm SUN Di, ZHU Wujun, XIANG Yanxun, et al. Advances in nonlinear ultrasonic detection of microcracks[J]. Chinese Science Bulletin, 2022, 67(7): 597-609. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB202207003.htm
[4]	MIAO H C, LI F X. Shear horizontal wave transducers for structural health monitoring and nondestructive testing: a review[J]. Ultrasonics, 2021, 114: 106355. doi: 10.1016/j.ultras.2021.106355
[5]	RAJAGOPAL P, LOWE M J S. Short range scattering of the fundamental shear horizontal guided wave mode normally incident at a through-thickness crack in an isotropic plate[J]. Journal of the Acoustical Society of America, 2007, 122(3): 1527-1538. doi: 10.1121/1.2764472
[6]	RAJAGOPAL P, LOWE M J S. Angular influence on the scattering of fundamental shear horizontal guided waves by a through-thickness crack in an isotropic plate[J]. Journal of the Acoustical Society of America, 2008, 124(4): 2021-2030. doi: 10.1121/1.2968697
[7]	RAJAGOPAL P, LOWE M J S. Scattering of the fundamental shear horizontal guided wave by a part-thickness crack in an isotropic plate[J]. Journal of the Acoustical Society of America, 2008, 124(5): 2895-2904. doi: 10.1121/1.2982410
[8]	RATASSEPP M, LOWE M J S, CAWLEY P, et al. Scattering of the fundamental shear horizontal mode in a plate when incident at a through crack aligned in the propagation direction of the mode[J]. Journal of the Acoustical Society of America, 2008, 124(5): 2873-2882. doi: 10.1121/1.2987426
[9]	陈洪磊, 刘增华, 李子明, 等. 有限单元法在超声导波检测技术中的应用[J]. 力学进展, 2020, 50: 202000. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ202000009.htm CHEN Honglei, LIU Zenghua, LI Ziming, et al. Application of flnite element method in ultrasonic guided waves testing technique[J]. Advances in Mechanics, 2020, 50: 202000. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ202000009.htm
[10]	戴海, 潘文峰. 谱元法求解Helmholtz方程透射特征值问题[J]. 应用数学和力学, 2018, 39(7): 833-840. doi: 10.21656/1000-0887.380327 DAI Hai, PAN Wenfeng. A spectral element method for transmission eigenvalue problems of the Helmholtz equation[J]. Applied Mathematics and Mechanics, 2018, 39(7): 833-840. (in Chinese) doi: 10.21656/1000-0887.380327
[11]	WEYLER R, OLIVER J, SAIN T, et al. On the contact domain method: a comparison of penalty and Lagrange multiplier implementations[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 205/208: 68-82. doi: 10.1016/j.cma.2011.01.011
[12]	SHEN Y F, CESNIK C E S. Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach[J]. Ultrasonics, 2017, 74: 106-123. doi: 10.1016/j.ultras.2016.10.001
[13]	PAPADOPOULOS P, SOLBERG J M. A Lagrange multiplier method for the finite element solution of frictionless contact problems[J]. Mathematical and Computer Modelling, 1998, 28(4/8): 373-384.
[14]	DE SAXCÉ G, FENG Z Q. New inequality and functional for contact with friction: the implicit standard material approach[J]. Mechanics of Structures and Machines, 1991, 19(3): 301-325. doi: 10.1080/08905459108905146
[15]	DE SAXCÉ G, FENG Z Q. The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms[J]. Mathematical and Computer Modelling, 1998, 28(4/8): 225-245.
[16]	CHEN H J, FENG Z Q, DU Y H, et al. Spectral finite element method for efficient simulation of nonlinear interactions between Lamb waves and breathing cracks within the bi-potential framework[J]. International Journal of Mechanical Science, 2022, 215: 106954. doi: 10.1016/j.ijmecsci.2021.106954
[17]	BERNARDI C, MADAY Y, PATERA A. A new nonconforming approach to domain decomposition: the mortar element method[J]. Nonlinear Partial Differential Equations and Their Applications, 1994, 24: 13-51.
[18]	CASADEI F, GABELLINI E, FOTIA G, et al. A mortar spectral finite element method for complex 2D and 3D elastodynamic problems[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(45): 5119-5148. doi: 10.1016/S0045-7825(02)00294-3
[19]	LI F L, ZOU F X. A hybrid spectral/finite element method for accurate and efficient modelling of crack-induced contact acoustic nonlinearity[J]. Journal of Sound and Vibration, 2021, 508: 116198. doi: 10.1016/j.jsv.2021.116198
[20]	EHRL A, POPP A, GRAVEMEIER V, et al. A dual mortar approach for mesh tying within a variational multiscale method for incompressible flow[J]. International Journal for Numerical Methods in Fluids, 2014, 76(1): 1-27. doi: 10.1002/fld.3920
[21]	CAVALIERI F J, CARDONA A. Numerical solution of frictional contact problems based on a mortar algorithm with an augmented Lagrangian technique[J]. Multibody System Dynamics, 2015, 35(4): 353-375.
[22]	PUSO M A, LAURSEN T A. A mortar segment-to-segment contact method for large deformation solid mechanics[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(6/8): 601-629.
[23]	PUSO M A. A 3D mortar method for solid mechanics[J]. International Journal for Numerical Methods in Engineering, 2004, 59(3): 315-336.
[24]	SIMO J C, LAURSEN T A. An augmented lagrangian treatment of contact problems involving friction[J]. Computers & Structures, 1992, 42(1): 97-116.
[25]	FENG Z Q, JOLI P, CROS J M, et al. The bi-potential method applied to the modeling of dynamic problems with friction[J]. Computational Mechanics, 2005, 36(5): 375-383.
[26]	周洋靖, 冯志强, 彭磊. 双势积分算法在非关联材料中的应用[J]. 应用数学和力学, 2018, 39(1): 11-28. doi: 10.21656/1000-0887.380139 ZHOU Yangjing, FENG Zhiqiang, PENG Lei. Application of the bi-potential integration algorithm to non-associated materials[J]. Applied Mathematics and Mechanics, 2018, 39(1): 11-28. (in Chinese) doi: 10.21656/1000-0887.380139
[27]	JOLI P, FENG Z Q. Uzawa and Newton algorithms to solve frictional contact problems within the bi-potential framework[J]. International Journal for Numerical Methods in Engineering, 2008, 73(3): 317-330.
[28]	吴斌, 张也驰, 郑阳, 等. 超声导波有限元仿真中吸收边界设置及参数[J]. 北京工业大学学报, 2013, 39(12): 1777-1783. https://www.cnki.com.cn/Article/CJFDTOTAL-BJGD201312004.htm WU Bin, ZHANG Yechi, ZHENG Yang, et al. Modeling and parameters of absorbing boundary for ultrasonic-guided wave in FE simulation[J]. Journal of Beijing University of Technology, 2013, 39(12): 1777-1783. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BJGD201312004.htm
[29]	杨启航, 李林安, 李利青, 等. 基于变分模态分解的结构裂纹识别[J]. 应用数学和力学, 2022, 43(12): 1324-1335. doi: 10.21656/1000-0887.420338 YANG Qihang, LI Lin'an, LI Liqing, et al. Structural crack identification based on the variational mode decomposition[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1324-1335. (in Chinese) doi: 10.21656/1000-0887.420338
[30]	WANG J S, XU C B, ZHAO Y X, et al. Characterization of microcrack orientation using the directivity of secondary sound source induced by an incident ultrasonic transverse wave[J]. Materials, 2020, 13(15): 3318.