[1] Zhao N. Research on ultrasonic nonlinear detection technology for micro metal fatigue damage[D](2015).

[2] Cantrell J H. Substructural organization, dislocation plasticity and harmonic generation in cyclically stressed wavy slip metals[J]. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 460, 757-780(2004).

[3] Wang Q. Research on Lamb wave and linear PZT array scanning based on directional damage imaging and evaluation[J]. Journal of Vibration,Measurement & Diagnosis, 37, 507-511, 628(2017).

[4] Lu M H, Xu X X. Review of nonlinear ultrasonic testing method[J]. Nondestructive Testing Technologying, 34, 61-66(2012).

[5] Dun Y, Shi X H, Wang G L et al. Nonlinear ultrasonic test of micro-nano crack[J]. Optics and Precision Engineering, 19, 132-137(2011).

[6] Qiao S, Zhu J X, Lü B L et al. Numerical simulation on damage assessment of micro cracks by ultrasonic nonlinearity[J]. Nondestructive Testing Technologying, 42, 50-55(2020).

[7] Deng M X, Pei J F. Nondestructive evaluation of fatigue damage in solid plates using nonlinear ultrasonic Lamb wave method[J]. Acta Acustica, 33, 360-369(2008).

[8] Deng M X, Xiang Y X, Pei J F et al. Time-domain measurement technique of second harmonic of ultrasonic Lamb waves using mismatch of group velocities[J]. Acta Acustica, 37, 621-628(2012).

[9] Tie Y, Zhang Q S, Hou Y L et al. Impact damage assessment in orthotropic CFRP laminates using nonlinear Lamb wave: Experimental and numerical investigations[J]. Composite Structures, 236, 111869(2020).

[10] Cao S H, Zhang H F, Xiong H Y et al. Research on plate crack detection based on nonlinear Lamb wave[C], 277-278(2019).

[11] Andreades C, Malfense Fierro G P, Meo M. A nonlinear ultrasonic SHM method for impact damage localisation in composite panels using a sparse array of piezoelectric PZT transducers[J]. Ultrasonics, 108, 106181(2020).

[12] Chen B B, Wang C, Wang P F et al. Research on fatigue damage in high-strength steel (FV520B) using nonlinear ultrasonic testing[J]. Shock and Vibration, 2020, 1-15(2020).

[13] Yang L J, Li Y, Sun J J et al. Reflection and transmission of laser ultrasonic waves on surface defects[J]. Laser & Optoelectronics Progress, 56, 041203(2019).

[14] Jiao J P, Li H P, Lü H T et al. Numerical simulation of nonlinear interaction between ultrasonic and micro-cracks in different directions[J]. Journal of Beijing University of Technology, 44, 708-715(2018).

[15] Kundu T, Eiras J N, Li W B et al. Fundamentals of nonlinear acoustical techniques and sideband peak count[M]. Kundu T. Nonlinear ultrasonic and vibro-acoustical techniques for nondestructive evaluation, 1-88(2019).

[16] Hu H F. Research on theory and key technologies of nonlinear ultrasonics for health monitoring of plate-like metallic structures[D](2011).

[17] Donskoy D, Sutin A, Ekimov A. Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing[J]. NDT & E International, 34, 231-238(2001).

[18] Yan H J, Liu F B, Pan Q X. Characterization of micro-crack in metal plane using nonlinear ultrasonic waves[J]. Modern Manufacturing Engineering, 17-21(2018).

[19] Wilcox P D, Holmes C, Drinkwater B W. Advanced reflector characterization with ultrasonic phased arrays in NDE applications[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 54, 1541-1550(2007).

[20] Yan S, Zhang H F, Meng Y Y. Numerical calculation and experimental validation for Lamb wave dispersion curves[J]. Journal of Huazhong University of Science and Technology (Urban Science Edition), 27, 1-4(2010).

[21] Dunne P C. Finite elements, procedures in engineering analysis: Kalus-Jurgen Bathe (Prentice-Hall, Englewood Cliffs, NJ, 1982)[J]. Computer Methods in Applied Mechanics and Engineering, 35, 123-124(1982).

[22] Lax P D. Hyperbolic difference equations: a review of the Courant-Friedrichs-Lewy paper in the light of recent developments[J]. IBM Journal of Research and Development, 11, 235-238(1967).