1. 1- Khadem SE, Rezaee M. An analytical approach for obtaining the location and depth of an all-over part-through crack on externally in-plane loaded rectangular plate using vibration analysis. Journal of Sound and Vibration. 2000;230(2):291-308. [
Link] [
DOI:10.1006/jsvi.1999.2619]
2. Khiem NT, Toan LK. A novel method for crack detection in beam-like structures by measurements of natural frequencies. Journal of Sound and Vibration. 2014;333(18):4084-4103. [
Link] [
DOI:10.1016/j.jsv.2014.04.031]
3. Mungla MJ, Sharma DS, Trivedi RR. Identification of a crack in clamped-clamped beam using frequency-based method and genetic algorithm. Procedia Engineering. 2016;144:1426-1434. [
Link] [
DOI:10.1016/j.proeng.2016.05.174]
4. Dahak M, Touat N, Benseddiq N. On the classification of normalized natural frequencies for damage detection in cantilever beam. Journal of Sound and Vibration. 2017;402:70-84. [
Link] [
DOI:10.1016/j.jsv.2017.05.007]
5. Cao M, Ye L, Zhou L, Su Z, Bai R. Sensitivity of fundamental mode shape and static deflection for damage identification in cantilever beams. Mechanical Systems and Signal Processing. 2011;25(2):630-643. [
Link] [
DOI:10.1016/j.ymssp.2010.06.011]
6. Nguyen KV. Mode shapes analysis of a cracked beam and its application for crack detection. Journal of Sound and Vibration. 2014;333(3):848-872. [
Link] [
DOI:10.1016/j.jsv.2013.10.006]
7. Dessi D, Camerlengo G. Damage identification techniques via modal curvature analysis: Overview and comparison. Mechanical Systems and Signal Processing. 2015;52-53:181-205. [
Link] [
DOI:10.1016/j.ymssp.2014.05.031]
8. Gelman L. The new frequency response functions for structural health monitoring. Engineering Structures. 2010;32(12):3994-3999. [
Link] [
DOI:10.1016/j.engstruct.2010.09.010]
9. Bandara RP, Chan THT, Thambiratnam DP. Frequency response function based damage identification using principal component analysis and pattern recognition technique. Engineering Structures. 2014;66:116-128. [
Link] [
DOI:10.1016/j.engstruct.2014.01.044]
10. Mohan SC, Maiti DK, Maity D. Structural damage assessment using FRF employing particle swarm optimization. Applied Mathematics and Computation. 2013;219(20):10387-10400. [
Link] [
DOI:10.1016/j.amc.2013.04.016]
11. Rezaee M, Fekrmandi H. Analysis of the nonlinear behavior of the free vibration of a cantilever beam with a fatigue crack using Lindstedt-Poincare's method. Amirkabir Journal of Mechanical Engineering. 2014;46(2):29-31. [
Link]
12. Rezaee M, Fekrmandi H. A theoretical and experimental investigation on free vibration behavior of a cantilever beam with a breathing crack. Shock and Vibration. 2012;19(2):175-186. [
Link] [
DOI:10.1155/2012/563916]
13. Na C, Kim SP, Kwak HG. Structural damage evaluation using genetic algorithm. Journal of Sound and Vibration. 2011;330(12):2772-2783. [
Link] [
DOI:10.1016/j.jsv.2011.01.007]
14. Li J, Wu B, Zeng QC, Lim CW. A generalized flexibility matrix based approach for structural damage detection. Journal of Sound and Vibration. 2010;329(22):4583-4587. [
Link] [
DOI:10.1016/j.jsv.2010.05.024]
15. Tsyfansky SL, Beresnevich VI. Detection of fatigue cracks in flexible geometrically non-linear bars by vibration monitoring. Journal of Sound and Vibration. 1998;213(1):159-168. [
Link] [
DOI:10.1006/jsvi.1998.1502]
16. El Bikri K, Benamar R, Bennouna MM. Geometrically non-linear free vibrations of clamped-clamped beams with an edge crack. Computers & Structures. 2006;84(7):485-502. [
Link] [
DOI:10.1016/j.compstruc.2005.09.030]
17. Merrimi EB, El Bikri K, Benamar R. Geometrically non-linear steady state periodic forced response of a clamped-clamped beam with an edge open crack. Comptes Rendus Mécanique. 2011;339(11):727-742. [
Link] [
DOI:10.1016/j.crme.2011.07.008]
18. Manoach E, Samborski S, Mitura A, Warminski J. Vibration based damage detection in composite beams under temperature variations using Poincaré maps. International Journal of Mechanical Sciences. 2012;62(1):120-132. [
Link] [
DOI:10.1016/j.ijmecsci.2012.06.006]
19. Stojanović V, Ribeiro P, Stoykov S. Non-linear vibration of Timoshenko damaged beams by a new p-version finite element method. Computers & Structures. 2013;120:107-119. [
Link] [
DOI:10.1016/j.compstruc.2013.02.012]
20. Carneiro GN, Ribeiro P. Vibrations of beams with a breathing crack and large amplitude displacements. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science. 2016;230(1):34-54. [
Link] [
DOI:10.1177/0954406215589333]
21. Majumder L, Manohar CS. Nonlinear reduced models for beam damage detection using data on moving oscillator-beam interactions. Computers & Structures. 2004;82(2-3):301-314. [
Link] [
DOI:10.1016/j.compstruc.2003.08.007]
22. Kitipornchai S, Ke LL, Yang J, Xiang Y. Nonlinear vibration of edge cracked functionally graded Timoshenko beams. Journal of Sound and Vibration. 2009;324(3-5):962-982. [
Link] [
DOI:10.1016/j.jsv.2009.02.023]
23. Chajdi M, Merrimi EB, ELBikri K. Geometrically nonlinear free vibration of composite materials: Clamped-clamped functionally graded beam with an edge crack using Homogenisation method. Key Engineering Materials. 2017;730:521-526. [
Link] [
DOI:10.4028/www.scientific.net/KEM.730.521]
24. Chajdi M, Merrimi EB, El Bikri Kh. Geometrically non-linear free and forced vibration of clamped-clamped functionally graded beam with discontinuities. Procedia Engineering. 2017;199:1870-1875. [
Link] [
DOI:10.1016/j.proeng.2017.09.117]
25. Nayfeh AH, Mook DT. Nonlinear oscillations. Hoboken: Wiley; 1979. [
Link] [
DOI:10.1115/1.3153771]
26. Meirovitch L. Analytical methods in vibrations. London: Macmillan; 1967. [
Link]
27. Lin HP, Chang SC, Wu JD. Beam vibrations with an arbitrary number of cracks. Journal of Sound and Vibration. 2002;258(5):987-999. [
Link] [
DOI:10.1006/jsvi.2002.5184]