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摘要:超声导波检测技术具有对波导结构中的缺陷进行远距离无损检测的能力,多年来一直是无损检测领域关注的热点之一.有限单元法具有对各种复杂动力学问题进行计算的能力,已成为超声导波检测技术研究的重要工具.本文结合超声导波检测技术研究领域中的热点问题,对相关的有限单元法进行了简要综述.介绍了有限单元法的发展及其在多物理场耦合机制下导波的激励与接收、线弹性和黏弹性结构中导波的传播特性、非线性超声导波等多个方面的应用研究情况. 最后,基于超声导波检测技术研究趋势展望了相关有限单元法的未来研究重点和发展方向.Abstract:Ultrasonic guided waves have the ability of long-distance nondestructive testing for defects in waveguide structures, and have been one of the hotspots in the field of nondestructive testing for many years. Finite element method (FEM) has the ability to calculate various complex dynamics problems and has become an important tool in the research of ultrasonic guided wave testing technique. Considering the hot issues in the research, a brief review of the relevant FEM is proposed. The development of FEM and its application in the excitation and reception of guided waves under multi-physical coupled field mechanism, the propagation characteristics of guided waves in linear elasticity and viscoelastic structures and nonlinear ultrasonic guided waves are introduced. Finally, the research emphasis and development direction of the relevant FEM in the future is prospected based on the research trend of ultrasonic guided wave testing technique.
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[1] 何存富, 吴斌, 范晋伟 . 2001. 超声柱面导波技术及其应用研究进展. 力学进展, 31:203-214(He C F, Wu B, Fan J W . 2001. Advances in ultrasonic cylindrical guided waves techniques and their applications. Adv. Mech., 31: 203-214). [2] 何存富, 郑明方, 吕炎, 邓鹏 . 2016. 超声导波检测技术的发展、应用与挑战. 仪器仪表学报, 37:1713-1735(He C F, Zheng M F, Lu Y, Deng P . 2016. Development, application and challenges in ultrasonic guided waves testing technology. Chin. J. Sci. Instru, 37: 1713-1735). [3] 刘瑶璐, 胡宁, 邓明晰, 赵友选 . 2017. 板壳结构中的非线性兰姆波. 力学进展, 47:507-537(Liu Y L, Hu N, Deng M X, Zhao Y X . 2017. Nonlinear Lamb waves in plate/shell structures. Adv. Mech., 47: 507-537). [4] 刘增华, 谢穆文, 钟栩文, 龚裕 . 2017. 超声导波电磁声换能器的研究进展. 北京工业大学学报, 43:192-202(Liu Z H, Xie M W, Zhong X W, Gong Y . 2017. Research progress of electromagnetic acoustic transducers for ultrasonic guided waves inspection. J. Beijing Univ. Technol., 43: 192-202). [5] 许伯强, 刘洪凯, 徐桂东, 徐晨光 . 2014. 基于应力-位移混合有限元法的激光超声数值模拟. 激光技术, 38:230-235(Xu B Q, Liu H K, Xu G F, Xu C G , 2014. Mixed stress-displacement finite element method for laser-generated ultrasound. Laser Technol., 38: 230-235). [6] Abedian A, Parvizian J, Duster A, Rank E. 2014. Finite cell method compared to h-version finite element method for elasto-plastic problems. Appl. Math. Mech. -Engl. Ed., 35:1239-1248. [7] Agrahari J, Kapuria S. 2016. Effects of adhesive, host plate, transducer and excitation parameters on time reversibility of ultrasonic Lamb waves. Ultrasonics, 70:147-157. [8] Ainsworth M. 2004. Discrete dispersion relation for hp-version finite element approximation at high wave number. SIAM J. Numer. Anal. , 42:553-575. [9] Ainsworth M, Wajid A H. 2010. Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. SIAM J. Numer. Anal., 48:346-371. [10] Allaire G, Jouve F, Toader A. 2003. Structural optimization using sensitivity analysis and a level-set method. J. Comp. Phys., 194:363-393. [11] Alleyne D, Cawley P. 1991. A two-dimensional Fourier transform method for the measurement of propagating multimode signals. J. Acoust. Soc. Am., 89:1159-1168. [12] Ashigwuike E C, Ushie O J, Mackay R, Balachandran W. 2015. A study of the transduction mechanisms of electromagnetic acoustic transducers (EMATs) on pipe steel materials. Sens. Actuator A-Phys., A229:154-165. [13] Augustyniak M, Usarek Z. 2016. Finite element method applied in electromagnetic NDTE: A review. J. Nondestruct. Eval., 35:1-15. [14] Avdiaj S, Setina J, Syla N. 2009. Modeling of the piezoelectric effect using the finite-element method. Mater. Tehnol., 43:283-291. [15] Babu?ka I, Ihlenburg F, Strouboulis T, Gangaraj S K. 1997 a. A posteriori error estimation for finite element solutions of Helmholtz equation: Part I The quality of local indicators and estimators. Int. J. Numer. Methods Eng., 40:3443-3462. [16] Babu?ka I, Ihlenburg F, Strouboulis T, Gangaraj S K. 1997 b. A posteriori error estimation for finite element solutions of Helmholtz equation: part II estimation of the pollution error. Int. J. Numer. Methods Eng., 40:3883-3900. [17] Babu?ka I, Osborn J E. 1983. Generalized finite element methods their performance and their relation to mixed methods. SIAM J. Numer. Anal., 20:510-536. [18] Babu?ka I M, Sauter S A. 1997. Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM J. Numer. Anal., 34:2392-2423. [19] Basri R, Chiu W. 2004. Numerical analysis on the interaction of guided Lamb waves with a local elastic stiffness reduction in quasi-isotropic composite plate structures. Compos. Struct., 66:87-99. [20] Bathe K J, Wilson E L. 1973. Stability and accuracy analysis of direct integration methods. Earthq. Eng. Struct. D., 1:283-291. [21] Bayliss A, Goldstein C, Turkel E. 1985. On accuracy conditions for the numerical computations of waves. J. Comput. Phys., 59:396-404. [22] Bartoli I, Marzani A, di Scalea F L, Viola E. 2006. Modeling wave propagation in damped waveguides of arbitrary cross-section. J. Sound Vibr., 295:685-707. [23] Belytschko T, Ong J S, Liu W K, Kennedy J M. 1984. Hourglass control in linear and nonlinear problems. Comput. Meth. Appl. Mech. Eng., 43:251-276. [24] Benjeddou A. 2000. Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Comput. Struct., 76:347-363. [25] Benmeddour F, Treyssede F, Laguerre L. 2011. Numerical modeling of guided wave interaction with non-axisymmetric cracks in elastic cylinders. Int. J. Solids Struct., 48:764-774. [26] Bhuiyan M Y, Shen Y F, Giurgiutiu V. 2017. Interaction of Lamb waves with rivet hole cracks from multiple directions. Proc. Inst. Mech. Eng. Part C-J. Eng. Mech. Eng. Sci., 231:2974-2987. [27] Bhuiyan Y, Shen Y F, Giurgiutiu V. 2016. Ultrasonic inspection of multiple-rivet-hole lap joint cracks using global analysis with local finite element approach// SPIE Conference on Health Monitoring of Structural and Biological Systems, March 21-24, 2016, Las Vegas, Clark, USA. [28] Blanloeuil P, Meziane A, Bacon C. 2014. Numerical study of the nonlinear interaction between a crack and elastic waves under an oblique incidence. Wave Motion, 51:425-437. [29] Broda D, Staszewski W, Martowicz A, Uhl T. 2014. Modelling of nonlinear crack-wave interactions for damage detection based on ultrasound—A review. J. Sound Vibr., 333:1097-1118. [30] Cantwell C, Moxey D, Comerford A, Bolis A. 2015. Nektar++: An open-source spectral hp element framework. Comput. Phys. Commun., 192:205-219. [31] Capuano G, Ruzzene M, Rimoli J J. 2018. Modal-based finite elements for efficient wave propagation analysis. Finite Elem. Anal. Des., 145:10-19. [32] Casadei F, Rimoli J, Ruzzene M. 2014. Multiscale finite element analysis of elastic wave scattering from localized defects. Finite Elem. Anal. Des., 88:1-15. [33] Casadei F, Rimoli J, Ruzzene M. 2016. Multiscale finite element analysis of wave propagation in periodic solids. Finite Elem. Anal. Des., 108:81-95. [34] Casadei F, Rimoli J J, Ruzzene M. 2013. A geometric multiscale finite element method for the dynamic analysis of heterogeneous solids. Comput. Meth. Appl. Mech. Eng., 263:56-70. [35] Casadei F, Ruzzene M. 2012. Frequency domain bridging method for wave propagation simulations in damaged structures. Wave Motion, 49:605-616. [36] Cawley P, Ada R D. 1979. The location of defects in structures from measurements of natural frequencies. J. Strain Anal., 14:49-57. [37] Cawley P. 2018. Structural health monitoring: Closing the gap between research and industrial deployment. Struct. Health Monit., 17:1225-1244. [38] Chakraborty A, Gopalakrishnan S. 2003. A spectrally formulated finite element for wave propagation analysis in functionally graded beams. Int. J. Solids Struct., 40:2421-2448. [39] Chaudhry Z, Rogers C. 1994. The pin-force model revisited. J. Intell. Mater. Syst. Struct., 5:347-354. [40] Chen J, Rostami J, Tse P W, Wan X. 2017. The design of a novel mother wavelet that is Tailor-made for continuous wavelet transform in extracting defect-related features from reflected guided wave signals. Measurement, 110:176-191. [41] Chen Y Y, Wu R X, Wang L H, Jing H M, Du J K, Hu Y T, Li G Q, Wang J. An analysis of nonlinear thickness-shear vibrations of quartz crystal plates using the two-dimensional finite element method. Mech. Adv. Mater. Struct., 25:395-406. [42] Chillara V K, Lissenden C J. 2014. Nonlinear guided waves in plates A numerical perspective. Ultrasonics, 54:1553-1558. [43] Chleboun J, Solin P. 2013. On optimal node and polynomial degree distribution in one-dimensional hp-FEM. Computing, 95:75-88. [44] Christides S, Barr A. 1984. One-dimensional theory of cracked Bernoulli-Euler beams. Int. J. Mech. Sci., 26:639-648. [45] Chronopoulos D. 2018. Calculation of guided wave interaction with nonlinearities and generation of harmonics in composite structures through a wave finite element method. Compos. Struct., 186:375-384. [46] Cottrell J A, Hughes T J R, Reali A. 2007. Studies of refinement and continuity in isogeometric structural analysis. Comput. Methods Appl. Mech. Engrg., 196:4160-4183. [47] Dauksher W, Emery A F. 1999. An evaluation of the cost effectiveness of Chebyshev spectral and p-finite element solutions to the scalar wave equation. Int. J. Numer. Methods Eng., 45:1099-1113. [48] Demma A, Cawley P, Lowe M, Pavlakovic B. 2005. The effect of bends on the propagation of guided waves in pipes. J. Press. Vessel Technol. -Trans. ASME, 127:328-335. [49] Devonshire A F. 1954. Theory of ferroelectrics. Adv. Phys., 3:85-130. [50] Dhayalan R, Balasubramaniam K. 2010. A hybrid finite element model for simulation of electromagnetic acoustic transducer (EMAT) based plate waves. NDT E Int., 43:519-526. [51] Dhayalan R, Kumar A, Rao B P. 2018. Numerical analysis of frequency optimization and effect of liquid sodium for ultrasonic high frequency guided wave inspection of core supportstructure of fast breeder reactor. Ann. Nucl. Energy, 115:233-242. [52] Doyle J. 1988. A spectrally formulated finite element for longitudinal wave propagation. Int. J. of Anal. and Exp. Mod. Anal., 3:1-5. [53] Droz C, Lainé J, Ichchou M, Inquiété G. 2014. A reduced formulation for the free-wave propagation analysis in composite structures. Compos. Struct., 113:134-144. [54] Duan W, Kirby R. 2015. A numerical model for the scattering of elastic waves from a non-axisymmetric defect in a pipe. Finite Elem. Anal. Des., 100: 28-40. [55] Duczek S, Joulaian M, Düster A, Gabbert U. 2014. Numerical analysis of Lamb waves using the finite and spectral cell methods. Int. J. Numer. Methods Eng., 99: 26-53. [56] Duczek S, Gabbert U. 2013. Anisotropic hierarchic finite elements for the simulation of piezoelectric smart structures. Eng. Comput., 30:682-706. [57] Duhamel D, Mace B R, Brennan M J. 2006. Finite element analysis of the vibrations of waveguides and periodic structures. J. Sound Vibr., 294:205-220. [58] Düster A, Broker H, Rank E. 2001. The p-version of the finite element method for three-dimensional curved thin walled structures. Int. J. Numer. Methods Eng., 52: 673-703. [59] Evans J A, Bazilevs Y, Babu?ka I, Hughes T J. 2009. n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric. Comput. Methods Appl. Mech. Engrg., 198: 1726-1741. [60] Fan Y, Collet M, Ichchou M, Li L. 2016. Energy flow prediction in built-up structures through a hybrid finite element/wave and finite element approach. Mech. Syst. Signal Proc., 66-67:137-158. [61] Flanagan D P, Belytschko T. 1981. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. Int. J. Numer. Methods Eng., 17:679-706. [62] Friswell M I, Penny J E T. 2002. Crack modeling for structural health monitoring. Struct. Health Monit., 1:139-148. [63] Furukawa T, Komura I, Language O. 2011. Simulation and visualization of guided wave propagation by large-scale 3D FEM. E-J. Adv. Maint., 3:92-101. [64] Galán J M, Abascal R. 2002. Numerical simulation of Lamb wave scattering in semi-infinite plates. Int. J. Numer. Meth. Engng., 53:1145-1173. [65] Gaudenzi P, Bathe K. 1995. An iterative finite element procedure for the analysis of piezoelectric continua. J. Intell. Mater. Syst. Struct., 6:266-273. [66] Ghandi K, Hagood N W. 1997. A hybrid finite element model for phase transitions in nonlinear electro-mechanically coupled material// Conference on Mathematics and Control in Smart Structures - Smart Structures and Materials. Mar 03-06, 1997, San Diego, California, USA. [67] Gravenkamp H, Natarajan S, Dornisch W. 2017. On the use of NURBS-based discretizations in the scaled boundary finite element method for wave propagation problems. Comput. Meth. Appl. Mech. Eng., 315:867-880. [68] Gresil M, Giurgiutiu V. 2013. Time-domain hybrid global-local concept for guided-wave propagation with piezoelectric wafer active sensor. J. Intell. Mater. Syst. Struct., 24:1897-1911. [69] Gresil M, Poohsai A, Chandarana N. 2016. Guided wave propagation and damage detection in composite pipes using piezoelectric sensors// 6th Asia-Pacific Workshop on Structural Health Monitoring. Dec 07-09, 2016, Hobart, Australia. [70] Guan R, Lu Y, Duan W, Wang X. 2017. Guided waves for damage identification in pipeline structures: A review. Struct. Control. Health Monit., 24:1-17. [71] Guddati M N, Yue B. 2004. Modified integration rules for reducing dispersion error in finite element methods. Comput. Methods Appl. Mech. Engrg., 193:275-287. [72] Guo H, Zheng B, Liu H. 2017. Numerical simulation and experimental research on interaction of micro-defects and laser ultrasonic signal. Opt. Laser Technol., 96:58-64. [73] Ha S, Chang F. 2010. Adhesive interface layer effects in PZT-induced Lamb wave propagation. Smart Mater. Struct., 19:25006. [74] Ha S, Chang F. 2010. Optimizing a spectral element for modeling PZT-induced Lamb wave propagation in thin plates. Smart Mater. Struct., 19:15015. [75] Ham S, Bathe K. 2012. A finite element method enriched for wave propagation problems. Comput. Struct., 94-95:1-12. [76] Han X, Liu G, Xi Z, Lam K. 2001. Transient waves in a functionally graded cylinder. Int. J. Solids Struct., 38:3021-3037. [77] Harding C, Hugo G, Bowles S. 2006. Model-assisted POD for ultrasonic detection of cracks at fastener holes// 32nd Annual Review of Process in Quantitative Nondestructive Evaluation, July 31-August 03, 2005, Brunswick, Cumberland, USA. [78] Hayashi T, Endoh S. 2000. Calculation and visualization of Lamb wave motion. Ultrasonics, 38:770-773. [79] He S, Ng C. 2015. Analysis of mode conversion and scattering of guided waves at cracks in isotropic beams using a time-domain spectral finite element method. Electron. J. Struct. Eng., 14:20-32. [80] Hedayatrasa S, Bui T Q, Zhang C, Lim C W. 2014. Numerical modeling of wave propagation in functionally graded materials using time-domain spectral Chebyshev elements. J. Comput. Phys., 258:381-404. [81] Heinlein S, Cawley P, Vogt T. 2018. Reflection of torsional T(0, 1) guided waves from defects in pipe bends. NDT E Int., 93:57-63. [82] Hong T K, Kennett B L N. 2002. On a wavelet-based method for the numerical simulation of wave propagation. J. Comput. Phys., 183:577-622. [83] Hosseini S M H, Kharaghani A, Kirsch C, Gabbert U. 2013. Numerical simulation of Lamb wave propagation in metallic foam sandwich structures: a parametric study. Compos. Struct., 97:387-400. [84] Hosseini S M H, Gabbert U. 2013. Numerical simulation of the Lamb wave propagation in honeycomb sandwich panels: A parametric study. Compos. Struct., 97:189-201. [85] Hosten B, Castaings M. 2006. FE modeling of Lamb mode diffraction by defects in anisotropic viscoelastic plates. NDT E Int., 39:195-204. [86] Hosten B, Moreau L, Castaings M. 2007. Signal processing to quantify the reflection/refraction of guided waves by a defect in viscoelastic plates. J. Acoust. Soc. Am., 894:587-594. [87] Ichchou M, Akrout S, Mencik J. 2007. Guided waves group and energy velocities via finite elements. J. Sound Vibr., 305:931-944. [88] Idesman A V, Schmidt M, Foley J R. 2011. Accurate finite element modeling of linear elastodynamics problems with the reduced dispersion error. Comput. Mech., 47:555-572. [89] Ihlenburg F, Babuska I. 1995. Finite element solution of the Helmholtz equation with high wave number Part I: The $h$-version of the FEM. Comput. Math. Appl., 30:9-37. [90] Ihlenburg F, Babuska I. 1997. Finite element solution of the Helmholtz equation with high wave number Part II: The $h$-$p$ version of the FEM. SIAM J. Numer. Anal., 34:315-358. [91] Jang I, Park I, Lee U. 2014. Guided waves in a Timoshenko beam with a bonded composite patch frequency domain spectral element modeling and analysis. Compos. Pt. B-Eng., 60:248-260. [92] Jensen S M. 1996. High convergence order finite elements with with lumped mass matrix. Int. J. Numer. Methods Eng., 39:1879-1888. [93] Jia X, Ouyang Q, Zhang X, Jiang X. 2017. An improved design of the spiral-coil EMAT for enhancing the signal amplitude. Sensors, 17: 1106(12pp). [94] Joglekar D, Mitra M. 2016. Analysis of flexural wave propagation through beams with a breathing crack using wavelet spectral finite element method. Mech. Syst. Signal Proc., 76:576-591. [95] Joulaian M, Duczek S, Gabbert U, Düster A. 2014. Finite and spectral cell method for wave propagation in heterogeneous materials. Comput. Mech., 54:661-675. [96] Kalkowski M K, Rustighi E, Waters T P. 2016. Modelling piezoelectric excitation in waveguides using the semi-analytical finite element method. Comput. Struct., 173:174-186. [97] Kawashima K. 1976. Theory and numerical calculation of the acoustic field produced in metal by an electromagnetic ultrasonic transducer. J. Acoust. Soc. Am., 60:1089-1099. [98] Kessentini A, Taktak M, Souf M B, Bareille O. 2016. Computation of the scattering matrix of guided acoustical propagation by the wave finite Element approach. Appl. Acoust., 108:92-100. [99] Khalili P, Cawley P. 2015. Excitation of single mode Lamb waves at high frequency thickness products. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 63:303-312. [100] Kim Y, Ha S, Chang F K. 2008. Time-domain spectral element method for built-in piezoelectric-actuator-induced Lamb wave propagation analysis. AIAA J. , 46:591-600. [101] Komatitsch D, Michéa D, Erlebacher G. 2009. Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA. J. Parallel Distrib. Comput., 69:451-460. [102] Komatitsch D, Tromp J. 1999. Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophys. J. Int., 139:806-822. [103] Komatitsch D, Vilot J. 1998. The spectral element methodan efficient tool to simulate the seismic response of 2D and 3D geological structures. Bull. Seismol. Soc. Amer., 88:368-392. [104] Koshiba M, Karakida S, Suzuki M. 1984. Finite-Element analysis of Lamb wave scattering in an elastic plate waveguide. IEEE T. Son. and Ultrason., 3:18-24. [105] Koshiba M, Morita H, Suzuki M. 1981. Finite element analysis of discontinuity problem of SH modes in an elastic plate waveguide. Electron. Lett., 17:480-482. [106] Kudela P, Ostachowicz W. 2009. 3D time-domain spectral elements for stress waves modelling// 7th International Conference on Modern Practice in Stress and Vibration Analysis, Sep 08-10, 2009, Murray Edwards Coll, Cambridge, England. [107] Kumar M, Pandit S. 2012. Wavelet transform and wavelet based numerical methods: An introduction. Int. J. nonlinear Sci., 13:325-345. [108] Lanzara G, Yoon Y, Kim Y, Chang F. 2009. Influence of interface degradation on the performance of piezoelectric actuators. J. Intell. Mater. Syst. Struct., 20:1699-1710. [109] Larcher N, Takarli M, Angellier N, Petit C. 2015. Towards a viscoelastic mechanical characterization of asphalt materials by ultrasonic measurements. Mater. Struct., 48:1377-1388. [110] Lee J H, Burger C P. 1995. Finite element modeling of laser-generated Lamb waves. Comput. Struct., 54:499-514. [111] Lee R, Andreas C C. 1992. A study of discretization error in the finite-element approximation of wave solutions. IEEE Trans. Antennas Propag., 40:542-549. [112] Lee U, Kim D, Park I. 2013. Dynamic modeling and analysis of the PZT-bonded composite Timoshenko beams: Spectral element method. J. Sound Vibr., 332:1585-1609. [113] Lee Y, Chung M. 2000. A study on crack detection using eigenfrequency test data. Comput. Struct., 77:327-342. [114] Li B, Chen X. 2014. Wavelet-based numerical analysis: A review and classification. Finite Elem. Anal. Des., 81:14-31. [115] Liu G R. 2002. A combined finite elementstrip element method for analyzing elastic wave scattering by cracks and inclusions in laminates. Comput. Mech., 28:76-82. [116] Liu G R, Tani J, Ohyoshi T, Watanabe K. 1991 a. Transient waves in anisotropic laminated plates. Part 1: Theory. J. Vib. Acoust. -Trans. ASME, 113:230-234. [117] Liu G R, Tani J, Ohyoshi T, Watanabe K. 1991 b. Transient waves in anisotropic laminated plates. Part 2: Application. J. Vib. Acoust. -Trans. ASME, 113:235-239. [118] Liu P, Nazirah A W, Sohn H. 2016. Numerical simulation of damage detection using laser-generated ultrasound. Ultrasonics, 69:248-258. [119] Liu W P, Giurgiutiu V. 2007. Finite element simulation of piezoelectric wafer active sensors for structural health monitoring with coupled-filed elements// Conference on Sensors and Smart Structures Technologies for Civil, Mechanical and Aerospace Systems, March 19-22, 2007, San Diego, California, USA. [120] Liu W, Hong J. 2015. Modeling of three-dimensional Lamb wave propagation excited by laser pulses. Ultrasonics, 55:113-122. [121] Liu Z H, Zhao J C, Wu B. 2010. Configuration optimization of magnetostrictive transducers for longitudinal guided wave inspection in seven-wire steel strands. NDT E Int., 43:484-492. [122] Liu Z H, Fan J W. 2015. Torsional mode magnetostrictive patch transducer array employing a modified planar solenoid array coil for pipe inspection. NDT E Int., 69:9-15. [123] Liu Z H, Hu Y N, Fan J W. 2016. Longitudinal mode magnetostrictive patch transducer array employing a multi-splitting meander coil for pipe inspection. NDT E Int., 79:30-37. [124] Liu Z H, Hu Y N, Xie M W. 2018 a. Development of omnidirectional $A_{0}$ mode EMAT employing a concentric permanent magnet pairs with opposite polarity for plate inspection. NDT E Int., 94:13-21. [125] Liu Z H, Zhang Y C. 2018 b. A direction-tunable shear horizontal mode array magnetostrictive patch transducer. NDT E Int., 97:20-31. [126] Loveday P W. 2007. Analysis of piezoelectric ultrasonic transducers attached to waveguides using waveguide finite elements. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 54:2045-2051. [127] Loveday P W. 2008. Simulation of piezoelectric excitation of guided waves using waveguide finite elements. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 55:2038-2045. [128] Lucena R L, D Santos. 2016. Structural health monitoring using time reversal and cracked rod spectral element. Mech. Syst. Signal Proc., 79:86-98. [129] Mace B R, Manconi E. 2008. Modelling wave propagation in two-dimensional structures using finite element analysis. J. Sound Vib., 318:884-902. [130] Marzani A. 2008. Time-transient response for ultrasonic guided waves propagating in damped cylinders. Int. J. Solids Struct., 45:6347-6368. [131] Gresil M, Giurgiutiu V. 2015. Prediction of attenuated guided waves propagation in carbon fiber composites using Rayleigh damping model. J. Intell. Mater. Syst. Struct., 26:2151-2169. [132] Mead D J. 1996. Wave propagation in continuous periodic structures research contributions from Southampton. J. Sound Vibr., 190:495-524. [133] Mead D J. 1975 a. Wave-propagation and natural modes in periodic systems. 1. Mono-coupled systems. J. Sound Vibr., 40:1-18. [134] Mead D J. 1975 b. Wave-propagation and natural modes in periodic systems. 2. Multi-coupled systems, with and without damping. J. Sound Vibr., 40:19-39. [135] Mitra M, Gopalakrishnan S. 2016. Guided wave based structural health monitoring: A review. Smart Mater. Struct., 25:53001. [136] Mitra M, Gopalakrishnan S. 2005. Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides. Int. J. Solids Struct., 42:4695-4721. [137] Moll J, Schulte R T, Hartmann B, Fritzen C. 2010. Multi-site damage localization in anisotropic plate-like structures using an active guidedwave structural health monitoring system. Smart Mater. Struct., 19:45022. [138] Moll J, Golub M V, Glushkov E, Glushkova N. 2012. Non-axisymmetric Lamb wave excitation by piezoelectric wafer active sensors. Sensors Actuat. A-Phys., 174:173-180. [139] Moreau L, Caleap M, Velichko A, Wilcox P D. 2011. Scattering of guided waves by through-thickness cavities with irregular shapes. Wave Motion, 48:586-602. [140] Mulder W. 1996. A comparison between higher-order finite elements and finite differences for solving the wave equation// 2nd ECCOMAS Conference on Numerical Methods in Engineering, Sep 09-13, 1996, Paris, France. [141] Narayanan D B, Beskos D E. 1978. Use of dynamic influence coefficients in forced vibration problems with the aid of fast Fourier transform. Comput. Struct., 9:145-150. [142] Ng C, Veidt M, Rose L, Wang C. 2012. Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates. J. Sound Vibr., 331:4870-4883. [143] Nieuwenhuis H, Neumann J, Greve W, Oppenheim J. 2005. Generation and detection of guided waves using PZT wafer transducers. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 52:2103-2111. [144] Ogi H. 1997. Field dependence of coupling efficiency between electromagnetic field and ultrasonic bulk waves. J. Appl. Phys., 82:3940-3949. [145] Oh O H, Sun K H, Kim Y Y. 2013. Time-harmonic finite element analysis of guided waves generated by magnetostrictive patch transducers. Smart Mater. Struct., 22:85007. [146] Ohara Y, Yamamoto S, Mihara T, Yamanaka K. 2008. Ultrasonic evaluation of closed cracks using subharmonic phased array. Jpn. J. Appl. Phys., 47:3908-3915. [147] Ong W H, Rajic N, Chiu W K, Rosalie C. 2018. Lamb wave-based detection of a controlled disbond in a lap joint. Struct. Health Monit., 17:668-683. [148] Ostachowicz W M. 2008. Damage detection of structures using spectral finite element method. Comput. Struct., 86:454-462. [149] Ostachowicz W, Kudela P, Krawczuk M. Guided waves in structures for SHM: The time-domain spectral element method. Hoboken: John Wiley & Sons, 2012: 47-92. [150] Pahlavan L, Mota M M, Blacquière G. 2016. Influence of asphalt on fatigue crack monitoring in steel bridge decks using guided waves. Constr. Build. Mater., 120:593-604. [151] Parvizian J, Düster A, Rank E. 2007. Finite cell method: $h$- and $p$-extension for embedded domain problems in solid mechanics. Comput. Mech., 41:121-133. [152] Patera A T. 1984. A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J. Comput. Phys., 54:468-488. [153] Pei C, Demachi K, Zhu H, Fukuchi T. 2012. Inspection of cracks using laser-induced ultrasound with shadow method: Modeling and validation. Opt. Laser Technol., 44:860-865. [154] Peng H, Meng G, Li F. 2009. Modeling of wave propagation in plate structures using three-dimensional spectral element method for damage detection. J. Sound Vibr., 320:942-954. [155] Radecki R, Su Z, Cheng L, Packo P. 2018. Modelling nonlinearity of guided ultrasonic waves in fatigued materials using a nonlinear local interaction simulation approach and a spring model. Ultrasonics, 84:272-289. [156] Ranjbar M, Mashayekhi M, Parvizian J, Düster A. 2014. Using the finite cell method to predict crack initiation in ductile materials. Comput. Mater. Sci., 82:427-434. [157] Rauter N, Lammering R. 2018. A constitutive model for the analysis of second harmonic Lamb waves in unidirectional composites. Int. J. Solids Struct., 135:184-196. [158] Rekatsinas C S, Saravanos D A. 2017. A cubic spline layerwise time domain spectral FE for guided wave simulation in laminated composite plate structures with physically modeled active piezoelectric sensors. Int. J. Solids Struct., 124:176-191. [159] Remo R, Frederic C, Peter N B, Peter C. 2010. Quantitative modeling of the transduction of electromagnetic acoustic transducers operating on ferromagnetic media. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 57:2808-2817. [160] Ren B, Lissenden C J. 2018. Modeling guided wave excitation in plates with surface mounted piezoelectric elements coupled physics and normal mode expansion. Smart Mater. Struct., 27:45014. [161] Renno J M, Mace B R. 2013. Calculation of reflection and transmission coefficients of joints using a hybrid finite element/wave and finite element approach. J. Sound Vib., 332:2149-2164. [162] Ribichini R, Cegla F, Nagy P, Cawley P. 2011. Experimental and numerical evaluation of electromagnetic acoustic transducer performance on steel materials. NDT E Int., 45:32-38. [163] Ribichini R, Nagy P, Ogi H. 2012. The impact of magnetostriction on the transduction of normal bias field EMATs. NDT E Int., 51:8-15. [164] Rong X Y, Lin P Y, Liu J Y, Yang T H. 2017. A new approach of waveform interpretation applied in nondestructive testing of defects in rock bolts based on mode identification. Math. Probl. Eng., 2017: 1-13. [165] Rose J L. 2018. Aspects of a hybrid analytical finite element method approach for ultrasonic guided wave inspection design. ASME J. Nondestr. Eval., Diagn. Prognostics Eng. Syst., 1:11001. [166] Rose J L. 2011. The upcoming revolution in ultrasonic guided waves// Conference on Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security, March 07-10, 2011, San Diego, California, USA. [167] Rouge C, Lhémery A, Aristégui C. 2014. Frequency spectra of magnetostrictive and Lorentz forces generated in ferromagnetic materials by a CW excited EMAT// 12th Annual Meeting on Anglo-French Physical Acoustics, January 16-18, 2013, Frejus, France. [168] Rucka M. 2010. Experimental and numerical study on damage detection in an L-joint using guided wave propagation. J. Sound Vibr., 329:1760-1779. [169] Ruess M, Tal D, Trabelsi N, Yosibash Z. 2012. The finite cell method for bone simulations: Verification and validation. Biomech. Model. Mechanobiol., 11:425-437. [170] Saravanos D, Heyliger P, Hopkins D. 1997. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int. J. Solids Struct., 34:359-378. [171] Satyarnarayan L, Chandrasekaran J, Maxfield B, Balasubramaniam K. 2008. Circumferential higher order guided wave modes for the detection and sizing of cracks and pinholes in pipe support regions. NDT E Int., 41:32-43. [172] Schmicker D. Development and testing of higher order finite elements based on Lagrange polynomials for the analysis of guided ultrasonic waves in thin walled structures. Saxony-Anhalt: Otto-von-Guericke-University Magdeburg, 2011. [173] Sébastien G, Christophe P, Christophe D, Jamal A. 2002. Design of optimal configuration for generating $A_{0}$ Lamb mode in a composite plate using piezoceramic transducers. J. Acoust. Soc. Am., 112:84-90. [174] Seifried R, Jacobs L, Qu J. 2002. Propagation of guided waves in adhesive bonded components. NDT E Int., 35:317-328. [175] Seung H M, Park C I, Kim Y Y. 2016. An omnidirectional shear-horizontal guided wave EMAT for a metallic plate. Ultrasonics, 69:58-66. [176] Shen Y F, Cesnik C E S. 2016. Modeling of fatigue crack induced nonlinear ultrasonics using a highly parallelized explicit local interaction simulation approach// SPIE Conference on Health Monitoring of Structural and Biological Systems, March 21-24, 2016, Las Vegas, Clark, UK. [177] Shen Y F, Cesnik C E S. 2016. Hybrid local FEM/global LISA modeling of damped guided wave propagation in complex composie structures. Smart Mater. Struct., 25:1-20. [178] Shen Y F. 2014. Structural health monitoring using linear and nonlinear ultrasonic guided waves. [PhD Thesis]. Columbia: University of South Carolina, 2014. [179] Shen Y F, Cesnik C E. 2017. Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach. Ultrasonics, 74:106-123. [180] Shen Y F, Giurgiutiu V. 2014. Predictive modeling of nonlinear wave propagation for structural health monitoring with piezoelectric wafer active sensors. J. of Int. Mater. and Syst. Struct., 25:506-520. [181] Shen Y F, Giurgiutiu V. 2016. Combined analytical FEM approach for efficient simulation of Lamb wave damage detection. Ultrasonics, 69:116-128. [182] Sikdar S, Banerjee S. 2016. Guided wave propagation in a honeycomb composite sandwich structure in presence of a high density core. Ultrasonics, 71:86-97. [183] Singh D, Castaings M, Bacon C. 2011. Sizing strip-like defects in plates using guided waves. NDT E Int., 44:394-404. [184] Solín P, Cerveny J, Dolezel I. 2008. Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM. Math. Comput. Simul., 77:117-132. [185] Solin P, Korous L. 2012. Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods. J. Comput. Phys., 231:1635-1649. [186] Soltani P, Akbareian N. 2014. Finite element simulation of laser generated ultrasound waves in aluminum plates. Lat. Am. J. Solids Struct., 11:1761-1776. [187] Song M, Jhang K, Yang Y. 2013. Crack detection in single-crystalline silicon wafer using laser generated Lamb wave. Adv. Mater. Sci. Eng., 2013: 1-6. [188] Soorgee M H, Lissenden C J, Rose J L , et al. 2013. Planar guided waves for SHM of plate structures using piezoelectric fiber transducers//39th Annual Review of Progress in Quantitative Nondestructive Evaluation, July 15-20, 2012, Denver, Colorado, USA. [189] Sridhar R, Chakraborty A, Gopalakrishnan S. 2006. Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method. Int. J. Solids Struct., 43:4997-5031. [190] Strouboulis T, Babuska I, Copps K. 2000. The design and analysis of the generalized finite element method. Comput. Meth. Appl. Mech. Eng., 181:43-69. [191] Su R L, Wang S J, Zhai G F. 2014. Numerical simulation of magnetostrictive Lamb wave EMATs on steel plate// 11th IEEE Far East Forum on Nondestructive Evaluation/Testing - New Technology and Application, June 20-23, 2014, Chengdu, Sichuang, China. [192] Sun H, Xu B, Qian R. 2009. Numerical simulation of laser-generated Lamb waves in viscoelastic. J. Appl. Phys., 106:73108. [193] Sun J, Lee K, Lee H. 2000. Comparison of implicit and explicit finite element methods for dynamic problems. J. Mater. Process. Technol., 105:110-118. [194] Surana K S. 1980. Transition finite elements for three-dimensional stress analysis. Int. J. Numer. Methods Eng., 15:991-1020. [195] Tchalla A, Belouettar S, Makradi A, Zahrouni H. 2013. An ABAQUS toolbox for multiscale finite element computation. Compos. Pt. B-Eng., 52:323-333. [196] Terrien N, Royer D, Lepoutre F, Déom A. 2007. Numerical predictions and experiments for optimizing hidden corrosion detection in aircraft structures using Lamb modes. Ultrasonics, 46:65-251. [197] Thompson R B. 1973. A model for the electromagnetic generation of ultrasonic guided waves in ferromagnetic metal polycrystals. IEEE Trans. Sonics Ultrason., 20:340-346. [198] Thompson R B, Brasche L H, Forsyth D , et al. 2009. Recent advances in model-assisted probability of detection// 4th European-American workshop on reliability of NDE, June 24-26, 2009, Berlin, Germany. [199] Vernerey F J, Kabiri M. 2012. An adaptive concurrent multiscale method for microstructured elastic solids. Comput. Meth. Appl. Mech. Eng., 241-244:52-64. [200] Wagner G J, Liu W K. 2003. Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys., 190:249-274. [201] Waki Y, Mace B, Brennan M. 2009. Numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides. J. Sound Vibr., 327:92-108. [202] Wan X, Zhang Q, Xu G, Tse P. 2014. Numerical simulation of nonlinear Lamb waves used in a thin plate for detecting buried micro-cracks. Sensors, 14:8528-8546. [203] Wang J, Yong Y K, Imai T. 1999. Finite element analysis of the piezoelectric vibrations of quartz plate resonators with higher-order plate theory. Int. J. Solids Struct., 36:2303-2319. [204] Wang J, Yu J D, Yong Y K, Imai T. 2000. A new theory for electrode piezoelectric plates and its finite element application for the forced vibrations of quartz crystal resonators. Int. J. Solids Struct., 37:5653-5673. [205] Wang J, Yu J D, Yong Y K, Imai T. 2008. A finite element analysis of frequency-temperature relations of AT-cut quartz crystal resonators with higher-order mindlin plate theory. Acta Mech. , 199:117-130. [206] Wang S, Li Z, Li P, Liu X. 2014. Numerical and experimental evaluation of the receiving performance of meander-line coil EMATs. Nondestruct. Test. Eva., 29:269-282. [207] Wang Y, Zhu X, Hao H, Ou J. 2011. Spectral element model updating for damage identification using clonal selection algorithm. Adv. Struct. Eng., 14:837-856. [208] Wilcox P D, Croxford A J, Konstantinidis G , et al. 2007. Sensitivity limitations for guided wave structural health monitoring// Conference on Health Monitoring of Structural and Biological Systems, March 19-22, 2007, San Diego, California, USA. [209] Willberg C, Duczek S, Perez J V, Schmicker D. 2012. Comparison of different higher order finite element schemes for the simulation of Lamb waves. Comput. Meth. Appl. Mech. Eng., 241:246-261. [210] Willberg C, Gabbert U. 2012. Development of a three dimensional piezoelectric isogeometric finite element for smart structure applications. Acta Mech., 223:1837-1850. [211] Willberg C, Duczek S, Perez J M V, Ahmad Z A B. 2015. Simulation methods for guided wave-based structural health monitoring: A review. Appl. Mech. Rev., 67:1-20. [212] Xiao D, Han Q, Liu Y, Li C. 2016. Guided wave propagation in an infinite functionally graded magneto-electro-elastic plate by the Chebyshev spectral element method. Compos. Struct., 153:704-711. [213] Xie Y, Yin W, Liu Z, Peytona A. 2016. Simulation of ultrasonic and EMAT arrays using FEM and FDTD. Ultrasonics, 66:154-165. [214] Xu B, Shen Z, Ni X, Lu J. 2004. Numerical simulation of laser-generated ultrasound by the finite element method. J. Appl. Phys., 95:2116-2122. [215] Yang J, Ume I C. 2008. Thermomechanical reliability study of flip-chip solder bumps: Using laser ultrasound technique and finite element method// 58th Electronic Components and Technology Conference, May 27-30, 2008, Orlando, Florida, USA. [216] Yang Z, Chen X, Xie Y, Zuo H. 2016. Wave motion analysis and modeling of membrane structures using the wavelet finite element method. Appl. Math. Model., 40:2407-2420. [217] Yu F, Collet M, Ichchou M, Lin L. 2017. Enhanced wave and finite element method for wave propagation and forced response prediction in periodic piezoelectric structures. Chin. J. Aeronaut., 30:75-87. [218] Yu X, Fan Z, Castaings M, Biateau C. 2017. Feature guided wave inspection of bond line defects between a stiffener and a composite plate. NDT E Int., 89:44-55. [219] Yu Y, Yan N. 2017. Numerical study on guided wave propagation in wood utility poles finite element modelling and parametric sensitivity analysis. Appl. Sci., 7:1063. [220] Yue B, Guddati M N. 2005. Dispersion-reducing finite elementsfor transient acoustics. J. Acoust. Soc. Am., 118:2132-2141. [221] Yuen M M F. 1985. A numerical study of the eigenparameters of a damaged cantilever. J. Sound Vib., 103:301-310. [222] Zander N, Kollmannsberger S, Ruess M, Yosibash Z. 2012. The Finite Cell Method for linear thermoelasticity. Comput. Math. Appl., 64:3527-3541. [223] Zhan Y, Liu C, Kong X, Lin Z. 2017. Experiment and numerical simulation for laser ultrasonic measurement of residual stress. Ultrasonics, 73:271-276. [224] Zhan Y, Liu C, Zhang F, Qiu Z. 2016. Experimental study and finite element analysis based on equivalent load method for laser ultrasonic measurement of elastic constants. Ultrasonics, 69:243-247. [225] Zhang X, Tang Z, Lü F, Yang K. 2017. Scattering of torsional flexural guided waves from circular holes and crack-like defects in hollow cylinders. NDT E Int., 89:56-66. [226] Zhou C W, Lainé J P, Ichchou M N, Zine A M. 2015. Wave finite element method based on reduced model for one-dimensional periodic structures. Int. J. Appl. Mech., 7:1550018. [227] Zhou J, Xiao L, Qu W, Lu Y. 2017. Nonlinear Lamb wave based DORT method for detection of fatigue cracks. NDT E Int., 92:22-29. [228] Zhu W. 2002. An FEM simulation for guided elastic wave generation and reflection in hollow cylinders with corrosion defects. J. Press. Vessel Technol. -Trans. ASME, 124:108-117. [229] Zhu W, Deng M, Xiang Y, Xuan F. 2016. Modeling of ultrasonic nonlinearities for dislocation evolution in plastically deformed materials: Simulation and experimental validation. Ultrasonics, 68:134-141.
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