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.
 W.T. Thomson, Vibration of slender bars with discontinuities in stiffness, J.Appl.Mech.16, (1949) 203-207.
 A.D. Dimarogonas, Vibration of cracked structures: A state of the art review, in, 1996.
 M. Krawczuk, W. Ostachowicz, Damage indicators for diagnostic of fatigue cracks in structures by vibration measurements: A survey, in, 1996.
 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.
 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.
 A. Bovsunovsky, C. Surace, Non-linearities in the vibrations of elastic structures with a closing crack: A state of the art review, in, 2015.
 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.
 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.
 H. Long, Y. Liu, K. Liu, Nonlinear Vibration Analysis of a Beam with a Breathing Crack, Applied Sciences, 9(18) (2019) 3874.
 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.
 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.
 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.
 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.
 S. Natsiavas, On the dynamics of oscillators with bi-linear damping and stiffness, International Journal of Non-Linear Mechanics, 25(5) (1990) 535-554.
 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.
 P.V. Bayly, On the spectral signature of weakly bilinear oscillators, (1996).
 J. Prawin, A.R.M. Rao, Development of polynomial model for cantilever beam with breathing crack, Procedia Engineering, 144 (2016) 1419-1425.
 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.
 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.
 M. Lalanne, P.a. Berthier, Mechanical vibrations for engineers, (1984).
 J. Prawin, A.R.M. Rao, Nonlinear System Identification of Breathing Crack Using Empirical Slow-Flow Model, (2019) 1075-1085.
 S.M. Cheng, A.S.J. Swamidas, X.J. Wu, W. Wallace, Vibrational response of a beam with a breathing crack, in, 1999.
 A.D. Dimarogonas, S.A. Paipetis, T.G. Chondros, Analytical methods in rotor dynamics, Springer Science & Business Media, 2013.
 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).
 H. Jeffreys, B. Jeffreys, B. Swirles, Methods of mathematical physics, Cambridge university press, 1999.
 A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008.
 A.H. Nayfeh, Introduction to perturbation techniques, John Wiley & Sons, 2011.
 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.
 A.P. Bovsunovsky, Efficiency of crack detection based on damping characteristics, Engineering Fracture Mechanics, 214 (2019) 464-473.
 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.