[1] Salawu OS (1997) Detection of structural damage through changes in frequency: a review. Eng Struct 19(9): 718-723.
[2] Maghsoodi A, Ghadami A, Mirdamadi HR (2013) Multiple-crack damage detection in multi-step beams by a novel local flexibility-based damage index. J Sound Vib 332(2): 294-305.
[3] Nahvi H, Jabbari M (2005) Crack detection in beams using experimental modal data and finite element model. Int J Mech Sci 47 (10): 1477-1497.
[4] Khorram A, Rezaeian M, Bakhtiari-Nejad F (2013) Multiple cracks detection in a beam subjected to a moving load using wavelet analysis combined with factorial design. Euro J Mech A/Solid 40: 97-113.
[5] Nguyen KV (2013) Comparison studies of open and breathing crack detections of a beam-like bridge subjected to a moving vehicle. Eng Struct 51: 306-314.
[6] Fan W, Qiao P (2013) Vibration-based Damage Identification Methods: A Review and Comparative Study. Struct Health Monit 10(1): 83-111.
[7] Moradi S, Razi P, Fatahi L (2011) On the application of bees algorithm to the problem of crack detection of beam-type structures. Comput Struct 89: 2169-2175.
[8] Vakil-Baghmisheh MT, Peimani M, Sadeghi MH, Ettefagh MM (2008) Crack detection in beam-like structures using genetic algorithms. Appl Soft Comput 8(2): 1150-1160.
[9] Moradi S, Kargozarfard MH (2013) On multiple crack detection in beam structures. J Mech Sci Tech 27(1): 47-55.
[10] Khaji N, Mehrjoo M (2014) Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms. J Mech Sci Tech 28(3): 823-836.
[11] Jena PK, Parhi DR (2015) A Modified Particle Swarm Optimization Technique for Crack Detection in Cantilever Beams. Arab J Sci Eng doi: 10.1007/s13369-015-1661-6
[12] Tada H, Paris P, Irwin G (1985) The Stress Analysis of Cracks Handbook. Research Corporation, Missouri.
[13] Torabi K, Dastgerdi JN, Marzban S (2012) Solution of free vibration equations of Euler-Bernoulli cracked beams by using differential transform method. Appl Mech Mater 110–116: 4532–4536.
[14] Yang X-S (2009) Firefly algorithms for multimodal optimization. Lecture notes in computer science 5792: 69–178.
[15] Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using Firefly Algorithm. Comput Struct 89: 2325–2336.
[16] Mirzabeigy A, Bakhtiari-Nejad F (2014) Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends. Front Mech Eng 9(2): 191–202.
[17] Patil DP, Maiti SK (2005) Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements. J Sound Vib 281: 439–451.