Crack identification of beam structures using homotopy continuation algorithm

References

• Abdel Wahab MM, De Roeck G. Damage detection in bridges using modal curvatures: application to a real damage scenario. J. Sound Vibr. 1999;226:217–235.
   Web of Science ®Google Scholar
• Douka E, Bamnios G, Trochidis A. A method for determining the location and depth of cracks in double-cracked beams. Appl. Acoust. 2004;65:997–1008.10.1016/j.apacoust.2004.05.002
   Web of Science ®Google Scholar
• Krawczuk M, Ostachowicz WM. Hexahedral finite element with an open crack. Finite Elem. Anal. Des. 1993;13:225–235.10.1016/0168-874X(93)90040-W
   Google Scholar
• Sinha JK, Friswell MI, Edwards S. Simplified models for the location of cracks in beam structures using measured vibration data. J. Sound Vibr. 2002;251:13–38.10.1006/jsvi.2001.3978
   Web of Science ®Google Scholar
• Chinchalkar S. Determination of crack location in beams using natural frequencies. J. Sound Vibr. 2001;247:417–429.10.1006/jsvi.2001.3748
   Web of Science ®Google Scholar
• Dilena M, Dell’Oste MF, Morassi A. Detecting cracks in pipes filled with fluid from changes in natural frequencies. Mech. Syst. Sig. Proc. 2011;25:3186–3197.10.1016/j.ymssp.2011.04.013
   Web of Science ®Google Scholar
• Rizos PF, Aspragathos N, Dimarogonas AD. Identification of crack location and magnitude in a cantilever beam from the vibration modes. J. Sound Vibr. 1990;138:381–388.10.1016/0022-460X(90)90593-O
   Web of Science ®Google Scholar
• Pandey AK, Biswas M. Damage detection in structures using change in flexibility. J. Sound Vibr. 1994;169:13–17.
   Web of Science ®Google Scholar
• Yang QW, Liu JK. Damage identification by the eigenparameter decomposition of structural flexibility change. Int. J. Numer. Methods Eng. 2009;78:444–459.10.1002/nme.v78:4
   Web of Science ®Google Scholar
• Cattarius J, Inman DJ. Time domain analysis for damage detection in smart structures. Mech. Syst. Sig. Proc. 1997;11:409–423.10.1006/mssp.1996.0086
   Web of Science ®Google Scholar
• Lu ZR, Law SS. Dynamic condition assessment of a cracked beam with the composite element model. Mech. Syst. Sig. Proc. 2009;23:415–431.10.1016/j.ymssp.2008.02.009
   Web of Science ®Google Scholar
• Lu XB, Liu JK, Lu ZR. A two-step approach for crack identification in beam. J. Sound Vibr. 2013;332:282–293.10.1016/j.jsv.2012.08.025
   Web of Science ®Google Scholar
• Bai RB, Song XG, Radzienski M, et al. Crack location in beams by data fusion of fractal dimension features of laser-measured operating deflection shapes. Smart Struct. Syst. 2014;13:975–991.10.12989/sss.2014.13.6.975
   Web of Science ®Google Scholar
• Bai RB, Ostachowicz W, Cao MS, et al. Crack detection in beams in noisy conditions using scale fractal dimension analysis of mode shapes. Smart Mater. Struct. 2014;23:065014.10.1088/0964-1726/23/6/065014
   Web of Science ®Google Scholar
• Eaves BC, Gould FJ, Peitgen HO, et al. Homotopy methods and global convergence. New York, NY: Plenum press; 1983.10.1007/978-1-4613-3572-6
   Google Scholar
• He JH. Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 2003;135:73–79.10.1016/S0096-3003(01)00312-5
   Web of Science ®Google Scholar
• Liao SJ. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 2004;147:499–513.10.1016/S0096-3003(02)00790-7
   Web of Science ®Google Scholar
• Alexander JC, Yorke JA. The homotopy continuation method: numerically implementable topological procedures. Trans. Am. Math. Soc. 1978;242:271–271.10.1090/S0002-9947-1978-0478138-5
   Web of Science ®Google Scholar
• Choi SH, Harney DA, Book NL. A robust path tracking algorithm for homotopy continuation. Comput. Chem. Eng. 1996;20:647–655.10.1016/0098-1354(95)00199-9
   Web of Science ®Google Scholar
• Iba K, Suzuki H, Egawa M, et al. Calculation of critical loading condition with nose curve using homotopy continuation method. IEEE Trans. Power Syst. 1991;6:584–593.10.1109/59.76701
   Web of Science ®Google Scholar
• Christides A, Barr ADS. One-dimensional theory of cracked Bernoulli–Euler beams. Int. J. Mech. Sci. 1984;26:639–648.10.1016/0020-7403(84)90017-1
   Web of Science ®Google Scholar
• Bathe kJ. Finite element procedures in engineering analysis. New Jersey: Prentice Hall; 1982.
   Google Scholar