Nego, D., Seordelis, A. (1967). Finite element analysis of reinforced concrete beam. Am. Con. Ins Journal, Vol. 63, pp. 240-252.
 Krishnamoorthy, C., Panneerselvam, S. A. (1978). FEP-ACSl-a finite element program for nonlinear analysis of reinforced concrete framed structures. Computer and Structures, Vol. 9, pp. 451–461.
 Zdenek, P. B., Byung, H. (1984). Deformation of progressively cracking reinforced concrete beams. Journal of ACI, Vol. 71, pp. 268–278.
 Hu, H., William, C. (1990). Nonlinear analysis of cracked reinforced concrete. Journal of ACI, Vol. 87, pp. 199–207.
 Krawczuk, M., Ostachowicz, W. M. (1995). Modelling and vibration analysis of a cantilever composite beam with a transverse open crack. Sound and Vibration, Vol. 183, pp. 69–89.
 Benarbia, D., Benguediab, M., Benguediab, S. (2013). Two-dimensional Analysis of Cracks Propagation in Structures of Concrete. Journal of Engineering, Technology & Applied Science Research, Vol. 3, pp. 429–432.
 Subramani, T., Manivannan, R., Kavitha, M. (2014). Crack Identification in Reinforced Concrete Beams Using Ansys Software. Engineering Research and Applications, Vol. 4, pp. 133–141.
 Slowik, M., Smarzewski, P. (2014). Numerical Modeling Of Diagonal Cracks In Concrete Beams. Archives of Civil Engineering, Vol. 3, pp. 307–322.
 Dimarogonas, A. D., Papadopulus, C. A. (1983). Vibration of cracked shafts in bending. Sound and Vibration, Vol. 91, pp. 583–593.
 Okamura, H., Liu, H. W., Chorng-Shin, C. (1969). A cracked column under compression. Engineering Fracture Mechanics, Vol. 1, pp. 547–564.
 Rizos, P. F., Aspragathos, N., Dimarogonas, A. D. (1990). Identification of crack location and magnitude in a cantilever beam from the vibration modes, Sound and Vibration, Vol. 3, pp. 381–388.
 Law, S. S., Zhu, X. Q. (2004). Dynamic behavior of damaged concrete bridge structures under moving vehicular loads. Engineering Structures, Vol. 26, pp. 1279–1293.
 Lee, J. (2010). Identification of a crack in a beam by the boundary element method. Mechanical Science and Technology, Vol. 24, pp. 801-804.
 Yokoyama, T., Chen, M. C. (1998). Vibration analysis of edge-cracked beams using a line-spring model. Engineering Fracture Mechanics, Vol. 59, pp. 403-409.
 Razzaghi, J., Abadi
, M. Kh., Alijani, A. (2018). A new approach to finite element modeling of crack in RC beams. Concrete research quarterly journal
, Vol. 11(2),
 Ricci, P., Viola, E. (2006). Stress intensity factors for cracked T-sections and dynamic behavior of T-beams. Engineering Fracture Mechanics, Vol. 73, pp. 91–111.
 Leissa, A. W. and Qatu, M. S. (2011). Vibrations of Continuous Systems. First edition, United States of America: McGraw-Hill, pp. 50-150.
 Rao, S. S. (2011). Mechanical Vibrations. Fifth edition, United States of America: Prentice Hall, pp. 22-57.
 Logan, D. L. (2007). A First Course in the Finite Element Method. Fourth edition, Canada: Thomson, pp. 78-121.
 Yokoyama, T. (1996). Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations. Journal of Computers & Structures, Vol. 61, pp. 995-1007.
 Gudmundsun, P. (1983). The dynamic behavior of slender structures with cross-sectional cracks. Mechanics and Physics of Solids, Vol. 1, pp. 329-345.
 Chaudhari, T. D., Maiti, S. K. (1999). Modelling of transverse vibration of beam of linearly variable depth with edge crack. Engineering Fracture Mechanics, Vol. 63, pp. 425-445.
 Pandey, A. K., Biswas, M. (1994). Damage detection in structures using changes in flexibility. Sound and Vibration, Vol. 169, pp. 3–17.
 Lele, S. P., Maiti, S. K. (2002). Modeling of transverse vibration of short beams for crack detection and measurement of crack extension. Sound and Vibration, Vol. 257, pp. 559-583.
 Silva, J. M., Gomes, A. J. (1990). Experimental dynamic analysis of cracked free-free beams. Experimental Mechanics, Vol. 30, pp. 20-25.
 Kim, J. T., Stubbs, N. (2003). Crack detection in beam-type structures using frequency data. Sound and Vibration, Vol. 259, pp. 145-160.
 Swamidas, A. S. J., Yang, X. F., Seshadri, R. (2004). Identification of cracking in beam structures using Timoshenko and Euler formulations. Engineering Mechanics, Vol. 130, pp. 1297-1308.
 Dobeling, S. W., Farrar, C. R., Prime, M. B. (1998). A summary review of vibration-based damage identification methods. Shock and Vibration Digest, Vol. 30, pp. 91-105.
 Cawly, P., Adams, R. D. (1979). The locations of defects in structures from measurements of natural frequencies. Strain Analysis, Vol. 14, pp. 49-57.
 Friswell, M. I., Penny, J. E. T., Wilson, D. A. L. (1994). Using vibration data and statistical measures to locate damage in structures. Experimental Techniques, Vol. 9, pp. 239-254.
 Narkis, Y. (1994). Identification of crack location in vibrating simply supported beams. Sound and Vibration, Vol. 172, pp. 549-558.
 Ratcliffe, C. P. (1997). Damage detection using a modified Laplacian operator on mode shape data. Sound and Vibration, Vol. 204, pp. 505-517.
 Ostachowicz, W. M., Krawczuk, M. (1991). Analysis of the cracks on the natural frequencies of a cantilever Beam. Sound and Vibration, Vol. 150, pp. 191-201.
 Binici, B. (2005). Vibration of beam with multiple open cracks subjected to axial force. Sound and Vibration, Vol. 287, pp. 277–295.
 Borst, R. D., Remmers, J. C., Needleman, A., Angèle Abellan, M. (2004). Discrete vs smeared crack models for concrete fracture: Bridging the gap. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 28(7-8), pp. 583 - 607.
 Chondros, T. G., Dimarogonas, A. D., Yao, J. (2001). Vibration of a beam with a breathing crack. Journal of Sound and vibration, Vol. 239(1), pp. 57-67.
 Liu, W., Barkey, M. E. (2018). The Effects of Breathing Behaviour on Crack Growth of a Vibrating Beam. Shock and Vibration, https://doi.org/10.1155/2018/2579419.
 Irwin, G. R., Kies, J. A. (1954). Critical energy rate analysis of fracture strength. Journal of Welding, Vol. 33(1), pp. 193–198.