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Nonlinear Vibration Analysis of Beam and Plate with Closed Crack: A Review

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1. Lin RM, Ng TY. Applications of higher-order frequency response functions to the detection and damage assessment of general structure systems with breathing cracks. Int J Mech Sci [Internet]. 2018;148:652-66. Available from: http://dx.doi.org/10.1016/j.ijmecsci.2018.08.02710.1016/j.ijmecsci.2018.08.027 Search in Google Scholar

2. Avci O, Abdeljaber O, Kiranyaz S, Hussein M, Gabbouj M, Inman DJ. A review of vibration-based damage detection in civil structures: From traditional methods to Machine Learning and Deep Learning applications. Mech Syst Signal Process [Internet]. 2021;147(107077):107077. Available from: http://dx.doi.org/10.1016/j.ymssp.2020.10707710.1016/j.ymssp.2020.107077 Search in Google Scholar

3. Antaki G, Gilada R. Chapter 2 - Design Basis Loads and Qualification, Editor(s): George Antaki, Ramiz Gilada, Nuclear Power Plant Safety and Mechanical Integrity. Butterworth-Heinemann; 2015.10.1016/B978-0-12-417248-7.00002-3 Search in Google Scholar

4. Webster M&., Clark L. The structural effects of corrosion - an overview of the mechanisms; 2000. Search in Google Scholar

5. Li YH, Dong YH, Qin Y, Lv HW. Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam. Int J Mech Sci [Internet]. 2018;138–139:131–45. Available from: http://dx.doi.org/10.1016/j.ijmecsci.2018.01.04110.1016/j.ijmecsci.2018.01.041 Search in Google Scholar

6. Galvão AS, Silva ARD, Silveira RAM, Gonçalves PB. Nonlinear dynamic behavior and instability of slender frames with semi-rigid connections. Int J Mech Sci [Internet]. 2010;52(12):1547–62. Available from: http://dx.doi.org/10.1016/j.ijmecsci.2010.07.00210.1016/j.ijmecsci.2010.07.002 Search in Google Scholar

7. Wang Y, Yang J, Moradi Z, Safa M, Khadimallah MA. Nonlinear dynamic analysis of thermally deformed beams subjected to uniform loading resting on nonlinear viscoelastic foundation. Eur J Mech A Solids [Internet]. 2022;95(104638):104638. Available from: http://dx.doi.org/10.1016/j.euromechsol.2022.10463810.1016/j.euromechsol.2022.104638 Search in Google Scholar

8. Prawin J, Rama Mohan Rao A. Vibration-based breathing crack identification using non-linear intermodulation components under noisy environment. Struct Health Monit [Internet]. 2020;19(1):86–104. Available from: http://dx.doi.org/10.1177/147592171983695310.1177/1475921719836953 Search in Google Scholar

9. Boungou D, Guillet F, Badaoui ME, Lyonnet P, Rosario T. Fatigue damage detection using cyclostationarity. Mech Syst Signal Process [Internet]. 2015;58–59:128–42. Available from: http://dx.doi.org/10.1016/j.ymssp.2014.11.01010.1016/j.ymssp.2014.11.010 Search in Google Scholar

10. Liu P, Sohn H. Damage detection using sideband peak count in spectral correlation domain. J Sound Vib [Internet]. 2017;411:20–33. Available from: http://dx.doi.org/10.1016/j.jsv.2017.08.04910.1016/j.jsv.2017.08.049 Search in Google Scholar

11. Hu C, Yiyong Y, Kexia P, Hu Y. The Vibration Characteristics Analysis of Damping System of Wall-mounted Airborne Equipment Based on FEM, IOP Conf. IOP Conf Ser: Earth Environ Sci. 2018.10.1088/1755-1315/108/2/022077 Search in Google Scholar

12. Oggu S, Sasmal S. Dynamic nonlinearities for identification of the breathing crack type damage in reinforced concrete bridges. Struct Health Monit. 2021;20(1):339–59.10.1177/1475921720930990 Search in Google Scholar

13. Wang X, Liu D, Zhang J, Jiao Y. Damage identification for nonlinear fatigue crack of cantilever beam under harmonic excitation. J vibroengineering [Internet]. 2022;435–52. Available from: http://dx.doi.org/10.21595/jve.2021.2218710.21595/jve.2021.22187 Search in Google Scholar

14. Ghadami A, Maghsoodi A, Mirdamad HR. A new adaptable multiple-crack detection algorithm in beam-like structures. Arch Mech. 2013;65(6):469–83. Search in Google Scholar

15. Sampath S, Sohn H. Detection and localization of fatigue crack using nonlinear ultrasonic three-wave mixing technique. Int J Fatigue [Internet]. 2022;155(106582):106582. Available from: http://dx.doi.org/10.1016/j.ijfatigue.2021.10658210.1016/j.ijfatigue.2021.106582 Search in Google Scholar

16. Zhao B, Xu Z, Kan X, Zhong J, Guo T. Structural damage detection by using single natural frequency and the corresponding mode shape. Shock Vib [Internet]. 2016;2016:1–8. Available from: http://dx.doi.org/10.1155/2016/819454910.1155/2016/8194549 Search in Google Scholar

17. Dilena M, Dell’Oste MF, Morassi A. Detecting cracks in pipes filled with fluid from changes in natural frequencies. Mech Syst Signal Process [Internet]. 2011;25(8):3186–97. Available from: http://dx.doi.org/10.1016/j.ymssp.2011.04.01310.1016/j.ymssp.2011.04.013 Search in Google Scholar

18. Mohan V, Parivallal S, Kesavan K, Arunsundaram B, Ahmed AKF, Ravisankar K. Studies on damage detection using frequency change correlation approach for health assessment. Procedia Eng [Internet]. 2014;86:503–10. Available from: http://dx.doi.org/10.1016/j.proeng.2014.11.07410.1016/j.proeng.2014.11.074 Search in Google Scholar

19. Gelman L, Gorpinich S, Thompson C. Adaptive diagnosis of the bilinear mechanical systems. Mech Syst Signal Process [Internet]. 2009;23(5):1548–53. Available from: http://dx.doi.org/10.1016/j.ymssp.2009.01.00710.1016/j.ymssp.2009.01.007 Search in Google Scholar

20. Giannini O, Casini P, Vestroni F. Nonlinear harmonic identification of breathing cracks in beams. Comput Struct [Internet]. 2013;129:166–77. Available from: http://dx.doi.org/10.1016/j.compstruc.2013.05.00210.1016/j.compstruc.2013.05.002 Search in Google Scholar

21. Caddemi S, Caliò I, Marletta M. The non-linear dynamic response of the Euler–Bernoulli beam with an arbitrary number of switching cracks. Int J Non Linear Mech [Internet]. 2010;45(7):714–26. Available from: http://dx.doi.org/10.1016/j.ijnonlinmec.2010.05.00110.1016/j.ijnonlinmec.2010.05.001 Search in Google Scholar

22. Chatterjee A. Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions. J Sound Vib [Internet]. 2010;329(16):3325–34. Available from: http://dx.doi.org/10.1016/j.jsv.2010.02.02610.1016/j.jsv.2010.02.026 Search in Google Scholar

23. Moore RC, Inan US, Bell TF. Observations of amplitude saturation in ELF/VLF wave generation by modulated HF heating of the auroral electrojet. Geophys Res Lett [Internet]. 2006;33(12). Available from: http://dx.doi.org/10.1029/2006gl02593410.1029/2006GL025934 Search in Google Scholar

24. Liu J, Zhu WD, Charalambides PG, Shao YM, Xu YF, Fang XM. A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips. J Sound Vib [Internet]. 2016;382:274–90. Available from: http://dx.doi.org/10.1016/j.jsv.2016.04.03610.1016/j.jsv.2016.04.036 Search in Google Scholar

25. Nitesh A, Vaibhav S. Analysis of crack detection of a cantilever beam using finite element analysis [IJERT. Int J Eng Res Technol (Ahmedabad). 2015;4(04):713–8.10.17577/IJERTV4IS041005 Search in Google Scholar

26. Kaushar HB, Sharma DS, Vishal V. Crack detection in cantilever beam by frequency-based method. Procedia Eng. 2013;51:770–5.10.1016/j.proeng.2013.01.110 Search in Google Scholar

27. Panteliou SD, Chondros TG, Argyrakis VC, Dimarogonas AD. Damping factor as an indicator of crack severity. J Sound Vib [Internet]. 2001;241(2):235–45. Available from: http://dx.doi.org/10.1006/jsvi.2000.329910.1006/jsvi.2000.3299 Search in Google Scholar

28. Zhang C, He L, Liu S, Yang Q. A new vibro-acoustic modulation technique for closed crack detection based on electromagnetic loading. Appl Acoust [Internet]. 2020;157(107004):107004. Available from: http://dx.doi.org/10.1016/j.apacoust.2019.10700410.1016/j.apacoust.2019.107004 Search in Google Scholar

29. Duffour P, Morbidini M, Cawley P. Comparison between a type of vibro-acoustic modulation and damping measurement as NDT techniques. NDT E Int [Internet]. 2006;39(2):123–31. Available from: http://dx.doi.org/10.1016/j.ndteint.2005.07.01010.1016/j.ndteint.2005.07.010 Search in Google Scholar

30. Jiao J, Zheng L, Song G, He C, Wu B. Vibro-acoustic modulation technique for micro-crack detection in pipeline. In: Fan K-C, Song M, Lu R-S, editors. Seventh International Symposium on Precision Engineering Measurements and Instrumentation [Internet]. SPIE; 2011. Available from: http://dx.doi.org/10.1117/12.90555010.1117/12.905550 Search in Google Scholar

31. Trochidis A, Hadjileontiadis L, Zacharias K. Analysis of Vibroacoustic Modulations for Crack Detection: A Time-Frequency Approach Based on Zhao-Atlas-Marks Distribution, Shock and Vibration; 2014.10.1155/2014/102157 Search in Google Scholar

32. Gelman L, Gorpinich S, Thompson C. Adaptive diagnosis of the bilinear mechanical systems. Mechanical Systems and Signal; 2009.10.1016/j.ymssp.2009.01.007 Search in Google Scholar

33. Cao MS, Sha GG, Gao YF, Ostachowicz W. Structural damage identification using damping: a compendium of uses and features. Smart Mater Struct [Internet]. 2017;26(4):043001. Available from: http://dx.doi.org/10.1088/1361-665x/aa550a10.1088/1361-665X/aa550a Search in Google Scholar

34. Wang Z, Lin RM, Lim MK. Structural damage detection using measured FRF data. Comput Methods Appl Mech Eng [Internet]. 1997;147(1–2):187–97. Available from: http://dx.doi.org/10.1016/s0045-7825(97)00013-310.1016/S0045-7825(97)00013-3 Search in Google Scholar

35. Cappello R, Cutugno S, Pitarresi G. Detection of crack-closure during fatigue loading by means of Second Harmonic Thermoelastic Stress Analysis. Procedia struct integr [Internet]. 2022;39:179–93. Available from: http://dx.doi.org/10.1016/j.prostr.2022.03.08710.1016/j.prostr.2022.03.087 Search in Google Scholar

36. Asnaashari E, Sinha JK. Development of residual operational deflection shape for crack detection in structures. Mech Syst Signal Process [Internet]. 2014;43(1–2):113–23. Available from: http://dx.doi.org/10.1016/j.ymssp.2013.10.00310.1016/j.ymssp.2013.10.003 Search in Google Scholar

37. Oks E, Dalimier E, Faenov A, Pikuz T, Fukuda Y, Andreev A, et al. Revealing the second harmonic generation in a femtosecond laser-driven cluster-based plasma by analyzing shapes of Ar XVII spectral lines. Opt Express [Internet]. 2015;23(25):31991–2005. Available from: http://dx.doi.org/10.1364/OE.23.03199110.1364/OE.23.03199126698990 Search in Google Scholar

38. Wei X, Zhongging S, Maosen C, Maciej R, Wiesla O. Nonlinear pseudo-force in a breathing crack to generate harmonics. J Sound Vibrat; 2021. Search in Google Scholar

39. Cao M, Su Z, Deng T, Xu W. Nonlinear pseudo-force in breathing delamination to generate harmonics: A mechanism and application study. Int J Mech Sci. 2021;192.10.1016/j.ijmecsci.2020.106124 Search in Google Scholar

40. Xu W, Su Z, Radzieński M, Cao M, Ostachowicz W. Nonlinear pseudo-force in a breathing crack to generate harmonics. J Sound Vib [Internet]. 2021;492(115734):115734. Available from: http://dx.doi.org/10.1016/j.jsv.2020.11573410.1016/j.jsv.2020.115734 Search in Google Scholar

41. Cui L, Xu H, Ge J, Cao M, Xu Y, Xu W, et al. Use of bispectrum analysis to inspect the non-linear dynamic characteristics of beam-type structures containing a breathing crack. Sensors (Basel) [Internet]. 2021;21(4):1177. Available from: http://dx.doi.org/10.3390/s2104117710.3390/s21041177791567933562385 Search in Google Scholar

42. Wang K, Liu M, Su Z, Yuan S, Fan Z. Analytical insight into “breathing” crack-induced acoustic nonlinearity with an application to quantitative evaluation of contact cracks. Ultrasonics [Internet]. 2018;88:157–67. Available from: http://dx.doi.org/10.1016/j.ultras.2018.03.00810.1016/j.ultras.2018.03.00829660569 Search in Google Scholar

43. Semperlotti F, Wang KW, Smith EC. Localization of a breathing crack using super-harmonic signals due to system nonlinearity. AIAA J [Internet]. 2009;47(9):2076–86. Available from: http://dx.doi.org/10.2514/1.3894710.2514/1.38947 Search in Google Scholar

44. Rivola A, White PR. Bispectral analysis of the bilinear oscillator with application to the detection of fatigue cracks. J Sound Vib [Internet]. 1998;216(5):889–910. Available from: http://dx.doi.org/10.1006/jsvi.1998.173810.1006/jsvi.1998.1738 Search in Google Scholar

45. Prawin J, Rao ARM. Development of polynomial model for cantilever beam with breathing crack. Procedia Eng [Internet]. 2016;144:1419–25. Available from: http://dx.doi.org/10.1016/j.proeng.2016.05.17310.1016/j.proeng.2016.05.173 Search in Google Scholar

46. Khalkar V, Ramachandran SV. Paradigm for natural frequency of an un-cracked cantilever beam and its application to cracked beam. Vibrations in Physical Systems; 2017. Search in Google Scholar

47. Chu YC, Shen MH. Analysis of Forced Bilinear Oscillators and the Application to Cracked Beam Dynam ics. AIAA J. 1992;30(10):2512–2251.10.2514/3.11254 Search in Google Scholar

48. Caddemi S, Caliò’ I. Exact solution of the multi-cracked Euler– Bernoulli column. Int J Solids Struct [Internet]. 2008;45(5):1332–51. Available from: http://dx.doi.org/10.1016/j.ijsolstr.2007.09.02210.1016/j.ijsolstr.2007.09.022 Search in Google Scholar

49. Dotti FE, Cortínez VH, Reguera F. Non-linear dynamic response to simple harmonic excitation of a thin-walled beam with a breathing crack. Appl Math Model [Internet]. 2016;40(1):451–67. Available from: http://dx.doi.org/10.1016/j.apm.2015.04.05210.1016/j.apm.2015.04.052 Search in Google Scholar

50. Bovsunovskii A, Surace C. Non-linearities in the vibrations of elastic structures with a closing crack: A state of the art review. Mech Syst Signal Process. 2015;129–48.10.1016/j.ymssp.2015.01.021 Search in Google Scholar

51. Broda D, Pieczonka L, Hiwarkar V, Staszewski WJ, Silberschmidt VV. Generation of higher harmonics in longitudinal vibration of beams with breathing cracks. J Sound Vib [Internet]. 2016;381:206–19. Available from: http://dx.doi.org/10.1016/j.jsv.2016.06.02510.1016/j.jsv.2016.06.025 Search in Google Scholar

52. Andreaus U, Baragatti P. Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response. J Sound Vib [Internet]. 2011;330(4):721–42. Available from: http://dx.doi.org/10.1016/j.jsv.2010.08.03210.1016/j.jsv.2010.08.032 Search in Google Scholar

53. Long H, Liu Y, Liu K. Nonlinear vibration analysis of a beam with a breathing crack. Appl Sci (Basel) [Internet]. 2019;9(18):3874. Available from: http://dx.doi.org/10.3390/app918387410.3390/app9183874 Search in Google Scholar

54. Pugno N, Surace C, Ruotolo R. Evaluation of the non-linear dynamic response to harmonic excitation of a beam with several breathing cracks. J Sound Vib [Internet]. 2000;235(5):749–62. Available from: http://dx.doi.org/10.1006/jsvi.2000.298010.1006/jsvi.2000.2980 Search in Google Scholar

55. Ji JC, Zhou J. Coexistence of two families of sub-harmonic resonances in a time-delayed nonlinear system at different forcing frequencies. Mech Syst Signal Process [Internet]. 2017;93:151–63. Available from: http://dx.doi.org/10.1016/j.ymssp.2017.02.00710.1016/j.ymssp.2017.02.007 Search in Google Scholar

56. Zhu J, Cai S, Suo Z. Resonant behavior of a membrane of a dielectric elastomer. Int J Solids Struct [Internet]. 2010;47(24):3254–62. Available from: http://dx.doi.org/10.1016/j.ijsolstr.2010.08.00810.1016/j.ijsolstr.2010.08.008 Search in Google Scholar

57. Casini P, Vestroni F, Giannini O. Crack detection in beam-like structures by nonlinear harmonic identification. Frat integrità strutt [Internet]. 2014;8(29):313–24. Available from: http://dx.doi.org/10.3221/igf-esis.29.2710.3221/IGF-ESIS.29.27 Search in Google Scholar

58. Zhao X, Zhao YR, Gao XZ, Li XY, Li YH. Green׳s functions for the forced vibrations of cracked Euler–Bernoulli beams. Mech Syst Signal Process [Internet]. 2016;68–69:155–75. Available from: http://dx.doi.org/10.1016/j.ymssp.2015.06.02310.1016/j.ymssp.2015.06.023 Search in Google Scholar

59. Zhao X, Chen B, Li YH, Zhu WD, Nkiegaing FJ, Shao YB. Forced vibration analysis of Timoshenko double-beam system under compressive axial load by means of Green’s functions. J Sound Vib [Internet]. 2020;464(115001):115001. Available from: http://dx.doi.org/10.1016/j.jsv.2019.11500110.1016/j.jsv.2019.115001 Search in Google Scholar

60. Chen B, Lin B, Zhao X, Zhu W, Yang Y, Li Y. Closed-form solutions for forced vibrations of a cracked double-beam system interconnected by a viscoelastic layer resting on Winkler–Pasternak elastic foundation. Thin-Walled Struct [Internet]. 2021;163(107688):107688. Available from: http://dx.doi.org/10.1016/j.tws.2021.10768810.1016/j.tws.2021.107688 Search in Google Scholar

61. Surace C, Ruotolo R, Storer D. Detecting nonlinear behavior using the volterra series to assess damage in beam-like structures; 2011. Search in Google Scholar

62. Yongfeng Y, Jianjun W, Yanlin W, Chao F, Qingyang Z, Kuan L. Dynamical analysis of hollow-shaft dual-rotor system with circular cracks. Low Freq Noise Vibr [Internet]. 2021;40(3):1227–40. Available from: http://dx.doi.org/10.1177/146134842094828710.1177/1461348420948287 Search in Google Scholar

63. Wang K, Li Y, Su Z, Guan R, Lu Y, Yuan S. Nonlinear aspects of “breathing” crack-disturbed plate waves: 3-D analytical modeling with experimental validation. Int J Mech Sci [Internet]. 2019;159:140–50. Available from: http://dx.doi.org/10.1016/j.ijmecsci.2019.05.03610.1016/j.ijmecsci.2019.05.036 Search in Google Scholar

64. Maruyama T, Saitoh T, Hirose S. Numerical study on sub-harmonic generation due to interior and surface breaking cracks with contact boundary conditions using time-domain boundary element method. Int J Solids Struct [Internet]. 2017;126–127:74–89. Available from: http://dx.doi.org/10.1016/j.ijsolstr.2017.07.02910.1016/j.ijsolstr.2017.07.029 Search in Google Scholar

65. Koskinen T, Kuutti J, Virkkunen I, Rinta-aho J. Online nonlinear ultrasound imaging of crack closure during thermal fatigue loading. NDT E Int [Internet]. 2021;123(102510):102510. Available from: http://dx.doi.org/10.1016/j.ndteint.2021.10251010.1016/j.ndteint.2021.102510 Search in Google Scholar

66. Lee SE, Hong JW. Detection of Micro-Cracks in Metals Using Modulation of PZT-Induced Lamb Waves. Materials (Basel). 2020;13.10.3390/ma13173823750403532872483 Search in Google Scholar

67. Wu TC, Kobayashi M, Tanabe M, Yang CH. The Use of Flexible Ultrasound Transducers for the Detection of Laser-Induced Guided Waves on Curved Surfaces at Elevated Temperaturs. Sensors (Basel). 2017;17.10.3390/s17061285 Search in Google Scholar

68. Lu Z, Dong D, Ouyang H, Cao S, Hua C. Localization of breathing cracks in stepped rotors using superharmonic characteristic deflection shapes based on singular value decomposition in frequency domain. Fatigue Fract Eng Mater Struct. 2017;40(11):1825–37.10.1111/ffe.12601 Search in Google Scholar

69. Cao M, Lu Q, Su Z, Radzieński M, Xu W, Ostachowicz W. A nonlinearity-sensitive approach for detection of “breathing” cracks relying on energy modulation effect. J Sound Vib [Internet]. 2022;524(116754):116754. Available from: http://dx.doi.org/10.1016/j.jsv.2022.11675410.1016/j.jsv.2022.116754 Search in Google Scholar

70. Sun X, Ding X, Li F, Zhou S, Liu Y, Hu N, et al. Interaction of Lamb wave modes with weak material nonlinearity: Generation of symmetric zero-frequency mode. Sensors (Basel) [Internet]. 2018;18(8). Available from: http://dx.doi.org/10.3390/s1808245110.3390/s18082451 Search in Google Scholar

71. Song H, Xiang M, Lu G, Wang T. Singular spectrum analysis and fuzzy entropy based damage detection on a thin aluminium plate by using PZTs. Smart Mater Struct. 2022;31(3).10.1088/1361-665X/ac4e53 Search in Google Scholar

72. Li W, Xu Y, Hu N, Deng M. Numerical and experimental investigations on second-order combined harmonic generation of Lamb wave mixing. AIP Adv [Internet]. 2020;10(4):045119. Available from: http://dx.doi.org/10.1063/1.514058810.1063/1.5140588 Search in Google Scholar

73. Zhu W, Xu Z, Xiang Y, Liu C, Deng M, Qiu X, et al. Nonlinear ultrasonic detection of partially closed cracks in metal plates using static component of lamb waves. NDT E Int [Internet]. 2021;124(102538):102538. Available from: http://dx.doi.org/10.1016/j.ndteint.2021.10253810.1016/j.ndteint.2021.102538 Search in Google Scholar

74. Chen B-Y, Soh S-K, Lee H-P, Tay T-E, Tan VBC. A vibro-acoustic modulation method for the detection of delamination and kissing bond in composites. J Compos Mater [Internet]. 2016;50(22):3089–104. Available from: http://dx.doi.org/10.1177/002199831561565210.1177/0021998315615652 Search in Google Scholar

75. Carneiro SHS, Inman DJ. Continuous model for the transverse vibration of cracked Timoshenko beams. J Vib Acoust [Internet]. 2002;124(2):310–20. Available from: http://dx.doi.org/10.1115/1.145274410.1115/1.1452744 Search in Google Scholar

76. Saito A. Nonlinear Vibration Analysis of Cracked Structures - Application to Turbomachinery Rotors with Cracked Blades. Turbomachinery Rotors with Cracked Blades; 2009. Search in Google Scholar

77. Rezaee M, Hassannejad R. Free vibration analysis of simply supported beam with breathing crack using perturbation method. Acta mech solida Sin [Internet]. 2010;23(5):459–70. Available from: http://dx.doi.org/10.1016/s0894-9166(10)60048-110.1016/S0894-9166(10)60048-1 Search in Google Scholar

78. Liu L, Mei X, Dong D, Liu H. Perturbation methods for dynamic analysis of cracked beams. In: 2011 International Conference on Consumer Electronics, Communications and Networks (CECNet). IEEE; 2011.10.1109/CECNET.2011.5768702 Search in Google Scholar

79. Stepanova LV, Igonin SA. Perturbation method for solving the nonlinear eigenvalue problem arising from fatigue crack growth problem in a damaged medium. Appl Math Model [Internet]. 2014;38(14):3436–55. Available from: http://dx.doi.org/10.1016/j.apm.2013.11.05710.1016/j.apm.2013.11.057 Search in Google Scholar

80. Kharazan M, Irani S, Noorian MA, Salimi MR. Nonlinear vibration analysis of a cantilever beam with multiple breathing edge cracks. Int J Non Linear Mech [Internet]. 2021;136(103774):103774. Available from: http://dx.doi.org/10.1016/j.ijnonlinmec.2021.10377410.1016/j.ijnonlinmec.2021.103774 Search in Google Scholar

81. Singh AC, Tay TE, Lee H. Numerical investigations of non-linear acoustics/ultrasonics for damage detection. 2016. Search in Google Scholar

82. Sun Z, Li F, Li H. A numerical study of non-collinear wave mixing and generated resonant components. Ultrasonics [Internet]. 2016;71:245–55. Available from: http://dx.doi.org/10.1016/j.ultras.2016.06.01910.1016/j.ultras.2016.06.01927403643 Search in Google Scholar

83. Tabatabaeipour M, Delrue J, Steven VA. Reconstruction Algorithm for Probabilistic Inspection of Damage (RAPID) in Composites. 2014. Search in Google Scholar

84. Andreades C, Malfense Fierro GP, Meo M. A nonlinear ultrasonic modulation approach for the detection and localisation of contact defects. Mech Syst Signal Process [Internet]. 2022;162(108088):108088. Available from: http://dx.doi.org/10.1016/j.ymssp.2021.10808810.1016/j.ymssp.2021.108088 Search in Google Scholar

85. Schwarts-Givli H, Rabinovitch O, Frostig Y. High-order nonlinear contact effects in the dynamic behavior of delaminated sandwich panels with a flexible core. Int J Solids Struct [Internet]. 2007;44(1):77–99. Available from: http://dx.doi.org/10.1016/j.ijsolstr.2006.04.01610.1016/j.ijsolstr.2006.04.016 Search in Google Scholar

86. Shankar G, Varuna JP. P.K.Mahato, Effect of delamination on vibration characteristic of smart laminated composite plate. Journal of Aerospace System Engineering. 2019;13(4):10–7. Search in Google Scholar

87. Mohammad H, Kargarnovin *., Ahmadian MT. Forced vibration of delaminated Timoshenko beams subjected to a moving load. Sci Eng Compos Mater. 2012;19(2):145–57.10.1515/secm-2011-0106 Search in Google Scholar

88. Zhang Z, Shankar K&., Murat & Morozov E. Vibration Modelling of Composite Laminates with Delamination Damage. ICCM International Conferences on Composite Material;. 2015. Search in Google Scholar

89. Chen Y, Huang B, Yan G, Wang J. Characterization of delamination effects on free vibration and impact response of composite plates resting on visco-Pasternak foundations. Int J Mech Sci. 2021. Search in Google Scholar

90. Thangaratnam K, Sanjana R. Nonlinear analysis of composite plates and shells subjected to in-plane loading. Appl Mech Mater [Internet]. 2018;877:341–6. Available from: http://dx.doi.org/10.4028/www.scientific.net/amm.877.34110.4028/www.scientific.net/AMM.877.341 Search in Google Scholar

91. Pradhan SC, Ng TY, Lam KY, Reddy JN. Control of laminated composite plates using magnetostrictive layers. Smart Mater Struct [Internet]. 2001;10(4):657–67. Available from: http://dx.doi.org/10.1088/0964-1726/10/4/30910.1088/0964-1726/10/4/309 Search in Google Scholar

92. Mantari JL, Oktem AS. Guedes Soares C. A new higher order shear deformation theory for sandwich and composite laminated plates. Part B Eng. 2012;43(3):1489–99.10.1016/j.compositesb.2011.07.017 Search in Google Scholar

93. Fares ME, Elmarghany MK. A refined zigzag nonlinear first-order shear deformation theory of composite laminated plates. Compos Struct [Internet]. 2008;82(1):71–83. Available from: http://dx.doi.org/10.1016/j.compstruct.2006.12.00710.1016/j.compstruct.2006.12.007 Search in Google Scholar

94. Yushu L, Zhou H, Huasong Q, Wenshan Y, Yilun L. Machine learning approach for delamination detection with feature missing and noise polluted vibration characteristics. Compos Struct. 2022; Search in Google Scholar

95. Civalek Ö. Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Compos B Eng [Internet]. 2013;50:171–9. Available from: http://dx.doi.org/10.1016/j.compositesb.2013.01.02710.1016/j.compositesb.2013.01.027 Search in Google Scholar

96. Civalek Ö. Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Compos B Eng [Internet]. 2013;50:171–9. Available from: http://dx.doi.org/10.1016/j.compositesb.2013.01.02710.1016/j.compositesb.2013.01.027 Search in Google Scholar

97. Shen H-S, Xiang Y. Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments. Eng Struct [Internet]. 2013;56:698–708. Available from: http://dx.doi.org/10.1016/j.engstruct.2013.06.00210.1016/j.engstruct.2013.06.002 Search in Google Scholar

98. Houhat N, Tournat V, Ménigot S, Boutkedjirt T, Girault J-M. Optimal pump excitation frequency for improvement of damage detection by nonlinear vibro acoustic modulation method in a multiple scattering sample. Appl Acoust [Internet]. 2019;155:222–31. Available from: http://dx.doi.org/10.1016/j.apacoust.2019.06.01010.1016/j.apacoust.2019.06.010 Search in Google Scholar

99. Zhang X, Wu X, He Y, Yang S, Chen S, Zhang S, et al. CFRP barely visible impact damage inspection based on an ultrasound wave distortion indicator. Compos B Eng [Internet]. 2019;168:152–8. Available from: http://dx.doi.org/10.1016/j.compositesb.2018.12.09210.1016/j.compositesb.2018.12.092 Search in Google Scholar

100. Castellano A, Fraddosio A, Piccioni MD, Kundu T. Linear and nonlinear ultrasonic techniques for monitoring stress-induced damages in concrete. J Nondestruct Eval Diagn Progn Eng Syst [Internet]. 2021;4(4):1–21. Available from: http://dx.doi.org/10.1115/1.405035410.1115/1.4050354 Search in Google Scholar

101. Santhakumar S, Hoon S. Detection and localization of fatigue crack using nonlinear ultrasonic three-wave mixing technique. Int J Fatigue. 2022; Search in Google Scholar

102. Qin W, Liyong Z, Jianguo Z, Lijun Z, Wenfeng H. Characterization of impact fatigue damage in CFRP composites using nonlinear acoustic resonance method. Compos Struct. 2020; Search in Google Scholar

103. Sikdar S, Ostachowicz W, Kudela P, Radzieński M. Barely visible impact damage identification in a 3D core sandwich structure. Computer Assisted Methods In Engineering And Science. 2018;24(4):259–68. Search in Google Scholar

104. Xianghong W, He C, He H, Wei X. Simulation and experimental research on nonlinear ultrasonic testing of composite material porosity. Appl Acoust. 2022;10.1016/j.apacoust.2021.108528 Search in Google Scholar

105. Yang F, Sedaghati R, Esmailzadeh E. Vibration suppression of structures using tuned mass damper technology: A state-of-the-art review. J Vib Control [Internet]. 2022;28(7–8):812–36. Available from: http://dx.doi.org/10.1177/107754632098430510.1177/1077546320984305 Search in Google Scholar

106. Buezas F, Rosales MB, Filipich C. Damage detection with genetic algorithms taking into account a crack contact model. Engineering Fracture Mechanics - ENG FRACTURE MECH. 2011;78:695–712.10.1016/j.engfracmech.2010.11.008 Search in Google Scholar

107. Shallan O, Atef &., Tharwat &., Khozam M. Structural DamageDetection using Genetic Algorithm by Static Measurements. International Journal of Trend Research Development. 2017;4:2394–9. Search in Google Scholar

108. Qi Y, Rui X, Ji K, Liu C, Zhou C. Study on aeolian vibration suppression schemes for large crossing span of ultra-high-voltage eight-bundle conductors. Adv Mech Eng [Internet]. 2019;11(4):168781401984270. Available from: http://dx.doi.org/10.1177/168781401984270610.1177/1687814019842706 Search in Google Scholar

109. Ashtiani M, Hashemabadi SH, Ghaffari A. A review on the magnetorheological fluid preparation and stabilization. J Magn Magn Mater [Internet]. 2015;374:716–30. Available from: http://dx.doi.org/10.1016/j.jmmm.2014.09.02010.1016/j.jmmm.2014.09.020 Search in Google Scholar

110. Williams K, Chiu G, Bernhard R. Adaptive-passive absorbers using shape-memory alloys. J Sound Vib [Internet]. 2002;249(5):835–48. Available from: http://dx.doi.org/10.1006/jsvi.2000.349610.1006/jsvi.2000.3496 Search in Google Scholar

111. Mohanty S, Dwivedy S. Linear and nonlinear analysis of traditional and non-traditional piezoelectric vibration absorber with time delay feedback for simultaneous resonance conditions. Mechanical Systems and Signal Processing. 2021.10.1016/j.ymssp.2021.107980 Search in Google Scholar

112. Zhang W, Zhao MH. Nonlinear vibrations of a composite laminated cantilever rectangular plate with one-to-one internal resonance. Nonlinear Dyn [Internet]. 2012;70(1):295–313. Available from: http://dx.doi.org/10.1007/s11071-012-0455-610.1007/s11071-012-0455-6 Search in Google Scholar

113. Yousuf LS. Nonlinear dynamics investigation of bending deflection of stiffened composite laminated plate using Lyapunov exponent conception. In: Volume 7B: Dynamics, Vibration, and Control. American Society of Mechanical Engineers; 2021.10.1115/IMECE2021-67448 Search in Google Scholar

114. Dauson E, Donahue C, DeWolf S, Hua L, Xiao H, Murdoch L, et al. Damage Detection in a laboratory-scale wellbore applying Time Reverse Nonlinear Elastic Wave Spectroscopy. TR NEWS; 2021. 115. Wei D, Liu X, Wang B, Tang Z, Bo L. Damage quantification of aluminum plates using SC-DTW method based on Lamb waves. Meas Sci Technol [Internet]. 2022;33(4):045001. Available from: http://dx.doi.org/10.1088/1361-6501/ac443510.1088/1361-6501/ac4435 Search in Google Scholar

116. Zhen P, Li J, Hao H, Li C. Nonlinear structural damage detection using output-only Volterra series model. Struct Contr Health Monit. 2021. Search in Google Scholar

117. Samaitis V, Mažeika L, Rekuvienė R. Assessment of the length and depth of delamination-type defects using ultrasonic guided waves. Appl Sci (Basel) [Internet]. 2020;10(15):5236. Available from: http://dx.doi.org/10.3390/app1015523610.3390/app10155236 Search in Google Scholar

118. Wang CH, Rose LRF. Wave reflection and transmission in beams containing delamination and inhomogeneity. J Sound Vib [Internet]. 2003;264(4):851–72. Available from: http://dx.doi.org/10.1016/s0022-460x(02)01193-810.1016/S0022-460X(02)01193-8 Search in Google Scholar

119. Nag A, Mahapatra D, Gopalakrishnan S, Sankar TS. A spectral finite element with embedded delamination for modeling of wave scattering in composite beams. Compos Sci Technol. 2003;63(15):2187–200.10.1016/S0266-3538(03)00176-3 Search in Google Scholar

120. Gudmundson P; GUDMUNSON. The dynamic behaviour of slender structures with cross-sectional cracks. J Mech Phys Solids. 1983;31(4):329–45.10.1016/0022-5096(83)90003-0 Search in Google Scholar

121. Zhang W, Ma H, Zeng J, Wu S, Wen B. Vibration responses analysis of an elastic-support cantilever beam with crack and offset boundary. Mech Syst Signal Process [Internet]. 2017;95:205–18. Available from: http://dx.doi.org/10.1016/j.ymssp.2017.03.03210.1016/j.ymssp.2017.03.032 Search in Google Scholar

122. Matveev VV, Boginich OE, Yakovlev AP. Approximate analytical method for determining the vibration-diagnostic parameter indicating the presence of a crack in a distributed-parameter elastic system at super- and subharmonic resonances. Strength Mater [Internet]. 2010;42(5):528–43. Available from: http://dx.doi.org/10.1007/s11223-010-9243-z10.1007/s11223-010-9243-z Search in Google Scholar