[1] P.G. Kirmser, The effect of discontinuities on the natural frequency of beams, Proceedings of the American Society of Testing and Materials, 44 (1944) 897-904.
[2] W.T. Thomson, Vibration of slender bars with discontinuities in stiffness, J.Appl.Mech.16, (1949) 203-207.
[3] A.D. Dimarogonas, Vibration of cracked structures: A state of the art review, in, 1996.
[4] M. Krawczuk, W. Ostachowicz, Damage indicators for diagnostic of fatigue cracks in structures by vibration measurements: A survey, in, 1996.
[5] P. Cawley, R. Ray, A comparison of the natural frequency changes produced by cracks and slots, Journal of vibration, acoustics, stress, and reliability in design, 110(3) (1988) 366-370.
[6] P. Gudmundson, Eigenfrequency changes of structures due to cracks, notches or other geometrical changes, Journal of the Mechanics and Physics of Solids, 30(5) (1982) 339-353.
[7] A. Bovsunovsky, C. Surace, Non-linearities in the vibrations of elastic structures with a closing crack: A state of the art review, in, 2015.
[8] A.P. Bovsunovskii, O.A. Bovsunovskii, Diagnostics of closing cracks in rodlike elements at nonlinear resonances by the method of variation of the asymmetry of driving forces, Strength of materials, 42(4) (2010) 397-405.
[9] D. Broda, L. Pieczonka, V. Hiwarkar, W.J. Staszewski, V.V. Silberschmidt, Generation of higher harmonics in longitudinal vibration of beams with breathing cracks, Journal of Sound and Vibration, 381 (2016) 206-219.
[10] H. Long, Y. Liu, K. Liu, Nonlinear Vibration Analysis of a Beam with a Breathing Crack, Applied Sciences, 9(18) (2019) 3874.
[11] C. Surace, R. Ruotolo, D. Storer, Detecting nonlinear behaviour using the Volterra series to assess damage in beam-like structures, Journal of Theoretical and applied mechanics, 49 (2011) 905-926.
[12] J. Prawin, K. Lakshmi, A.R.M. Rao, A novel vibration based breathing crack localization technique using a single sensor measurement, Mechanical Systems and Signal Processing, 122 (2019) 117-138.
[13] P. Cacciola, N. Impollonia, G. Muscolino, Crack detection and location in a damaged beam vibrating under white noise, Computers & structures, 81(18-19) (2003) 1773-1782.
[14] A. Rivola, P.R. White, Bispectral analysis of the bilinear oscillator with application to the detection of fatigue cracks, Journal of Sound and Vibration, 216(5) (1998) 889-910.
[15] S. Natsiavas, On the dynamics of oscillators with bi-linear damping and stiffness, International Journal of Non-Linear Mechanics, 25(5) (1990) 535-554.
[16] Y.C. Chu, M.H. Shen, Analysis of forced bilinear oscillators and the application to cracked beam dynamics, AIAA journal, 30(10) (1992) 2512-2519.
[17] P.V. Bayly, On the spectral signature of weakly bilinear oscillators, (1996).
[18] J. Prawin, A.R.M. Rao, Development of polynomial model for cantilever beam with breathing crack, Procedia Engineering, 144 (2016) 1419-1425.
[19] W. Liu, M.E. Barkey, Nonlinear vibrational response of a single edge cracked beam, Journal of Mechanical Science and Technology, 31(11) (2017) 5231-5243.
[20] M. Kharazan, S. Irani, M.A. Noorian, M.R. Salimi, Effect of a breathing crack on the damping changes in nonlinear vibrations of a cracked beam: Experimental and theoretical investigations, Journal of Vibration and Control, (2020) 1077546320960312.
[21] M. Lalanne, P.a. Berthier, Mechanical vibrations for engineers, (1984).
[22] J. Prawin, A.R.M. Rao, Nonlinear System Identification of Breathing Crack Using Empirical Slow-Flow Model, (2019) 1075-1085.
[23] S.M. Cheng, A.S.J. Swamidas, X.J. Wu, W. Wallace, Vibrational response of a beam with a breathing crack, in, 1999.
[24] A.D. Dimarogonas, S.A. Paipetis, T.G. Chondros, Analytical methods in rotor dynamics, Springer Science & Business Media, 2013.
[25] A.E. Ismail, Mode I stress intensity factors of sickle-shaped surface cracks in round solid bars under bending moment., International Journal of Automotive & Mechanical Engineering, 13(2) (2016).
[26] H. Jeffreys, B. Jeffreys, B. Swirles, Methods of mathematical physics, Cambridge university press, 1999.
[27] A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008.
[28] A.H. Nayfeh, Introduction to perturbation techniques, John Wiley & Sons, 2011.
[29] A.P. Bovsunovskii, C. Surace, O.A. Bovsunovskii, The effect of damping and force application point on the non-linear dynamic behavior of a cracked beam at sub-and superresonance vibrations, Strength of materials, 38(5) (2006) 492-497.
[30] A.P. Bovsunovsky, Efficiency of crack detection based on damping characteristics, Engineering Fracture Mechanics, 214 (2019) 464-473.
[31] R. Ruotolo, C. Surace, P. Crespo, D. Storer, Harmonic analysis of the vibrations of a cantilevered beam with a closing crack, Computers & structures, 61(6) (1996) 1057-1074.
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