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Adaptive Finite Element Algorithm for Damage Detection of Non-Uniform Euler-Bernoulli Beams with Multiple Cracks Based on Natural Frequencies

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Adaptive Analysis of Damage and Fracture in Rock with Multiphysical Fields Coupling
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Abstract

In this chapter, the adaptive finite element algorithm for damage detection in non-uniform Euler-Bernoulli beams with multiple cracks, using natural frequencies, is introduced.

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References

  • Al-Said SM (2007) Crack identification in a stepped beam carrying a rigid disk. J Sound Vib 300(3):863–876

    Article  Google Scholar 

  • Al-Said SM (2008) Crack detection in stepped beam carrying slowly moving mass. J Sound Vib 14(12):1903–1920

    Google Scholar 

  • Caddemi S, Caliò I (2014) Exact reconstruction of multiple concentrated damages on beams. Acta Mech 225(11):3137–3156

    Article  Google Scholar 

  • Caddemi S, Morassi A (2013) Multi-cracked Euler-Bernoulli beams: mathematical modeling and exact solutions. Int J Solids Struct 50(6):944–956

    Article  Google Scholar 

  • Chaudhari TD, Maiti SK (2000) A study of vibration of geometrically segmented beams with and without crack. Int J Solids Struct 37(5):761–779

    Article  Google Scholar 

  • Chinchalkar S (2001) Determination of crack location in beams using natural frequencies. J Sound Vib 247(3):417–429

    Article  Google Scholar 

  • Clough RW, Penzien J (1993) Dynamics of structures, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Dado MH (1997) A comprehensive crack identification algorithm for beam under different end conditions. App Acoust 51(4):381–398

    Article  Google Scholar 

  • Dimarogonas AD (1996) Vibration of cracked structures: a state of the art review. Eng Fract Mech 55(5):831–857

    Article  Google Scholar 

  • Farrar CR, Doebling SW, Nix DA (2001) Vibration-based structural damage identification. Philos Trans R Soc 359(1778):131–149

    Article  Google Scholar 

  • Greenberg L, Marletta M (1997) Algorithm 775: The code SLEUTH for solving fourth order Sturm-Liouville problems. ACM Trans Math Softw 23(4):453–493

    Article  Google Scholar 

  • Guan H, Karbhari KM (2008) Improved damage detection method based on element modal strain damage index using sparse measurement. J Sound Vib 309(3):465–494

    Article  Google Scholar 

  • Hassiotis S, Jeong GD (1993) Assessment of structural damage from natural frequency measurements. Comput Struct 49(4):679–691

    Article  Google Scholar 

  • Hsu MH (2005) Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method. Comput Meth Appl Mech Eng 194(1):1–17

    Article  Google Scholar 

  • Hu J, Liang RY (1993) An integrated approach to detection of cracks using vibration characteristics. J Franklin Inst 330(5):841–853

    Article  Google Scholar 

  • Kaveh A, Dadfar B (2007) Eigensolution for free vibration of planar frames by weighted graph symmetry. Int J Num Meth Eng 69(6):1305–1330

    Article  Google Scholar 

  • Labib A, Kennedy D, Featherston C (2014) Free vibration analysis of beams and frames with multiple cracks for damage detection. J Sound Vib 333(20):4991–5003

    Article  Google Scholar 

  • Labib A, Kennedy D, Featherston CA (2015) Crack localisation in frames using natural frequency degradations. Comput Struct 157:51–59

    Article  Google Scholar 

  • Lee J (2009) Identification of multiple cracks in a beam using natural frequencies. J Sound Vib 320(3):482–490

    Google Scholar 

  • Lele SP, Maiti SK (2002) Modelling of transverse vibration of short beams for cracks detection and measurement of crack extension. J Sound Vib 257(3):559–583

    Article  Google Scholar 

  • Litewka P, Rakowski J (2001) Free vibrations of shear-flexible and compressible arches by FEM. Int J Num Meth Eng 52(3):273–286

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Moezi SA, Zakeri E, Zare A, Nedaeib M (2015) On the application of modified cuckoo optimization algorithm to the crack detection problem of cantilever Euler-Bernoulli beam. Comput Struct 157:42–50

    Article  Google Scholar 

  • Morassi A (2001) Identification of a crack in a rod based on changes in a pair of natural frequencies. J Sound Vib 242(4):577–596

    Article  Google Scholar 

  • Nandwana BP, Maiti SK (1997) Detection of the location and size of a crack in stepped cantilever beams based on measurements of natural frequencies. J Sound Vib 203(3):435–446

    Article  Google Scholar 

  • Narkis Y (1994) Identification of crack location in vibrating simply supported beams. J Sound Vib 172(4):549–558

    Article  Google Scholar 

  • Nikolakopoulos PG, Katsareas DE, Papadopoulos CA (1997) Crack identification in frame structures. Comput Struct 64(1–4):389–406

    Article  Google Scholar 

  • Owolabi GM, Swamidas ASJ, Seshadri R (2003) Crack detection in beams using changes in frequencies and amplitudes of frequency response functions. J Sound Vib 265(1):1–22

    Article  Google Scholar 

  • Patil DP, Maiti SK (2003) Detection of multiple cracks using frequency measurements. Eng, Frac, Mech 70(12):1553–1572

    Article  Google Scholar 

  • Pawar PM, Ganguli R (2003) Genetic fuzzy system for damage detection in beams and helicopter rotor blades. Comput Meth Appl Mech Eng 192(16–18):2031–2057

    Article  Google Scholar 

  • Rizos PF, Aspragathos N, Dimarogonas AD (1990) Identification of crack location and magnitude in a cantilever beam from the vibration modes. J Sound Vib 138(3):381–388

    Article  Google Scholar 

  • Ruotolo R, Surace C (1997) Damage assessment of multiple cracked beams: numerical results and experimental validation. J Sound Vib 206(4):567–588

    Article  Google Scholar 

  • Shifrin EI, Ruotolo R (1999) Natural frequencies of a beam with an arbitrary number of cracks. J Sound Vib 222(3):409–423

    Article  Google Scholar 

  • Wang D, Liu W, Zhang H (2015) Superconvergent isogeometric free vibration analysis of Euler-Bernoulli beams and Kirchhoff plates with new higher order mass matrices. Comput Meth Appl Mech Eng 286:230–267

    Article  Google Scholar 

  • Wang Y, Liu Z, Yang H, Zhuang Z (2017a) Finite element analysis for wellbore stability of transversely isotropic rock with hydraulic-mechanical-damage coupling. Sci Chi Tech Sci 60(1):133–145

    Article  Google Scholar 

  • Wang Y, Zhuang Z, Liu Z, Yang H, Li C (2017b) Finite element analysis for inclined wellbore stability of transversely isotropic rock with HMCD coupling based on weak plane strength criterion. Sci Chi Tech Sci 60(4):624–637

    Article  Google Scholar 

  • Wang Z, Lin RM, Lim MK (1997) Structural damage detection using measured FRF data. Comput Meth Appl Mech Eng 147(1–2):187–197

    Article  Google Scholar 

  • Wiberg NE, Bausys R, Hager P (1999a) Adaptive h-version eigenfrequency analysis. Comput Struct 71(5):565–584

    Article  Google Scholar 

  • Wiberg NE, Bausys R, Hager P (1999b) Improved eigenfrequencies and eigenmodes in free vibration analysis. Comput Struct 73(1–5):79–89

    Article  Google Scholar 

  • Yan W, Chen WQ, Cai JB, Lim CW (2007) Quantitative structural damage detection using high-frequency piezoelectric signatures via the reverberation matrix method. Int J Nu Meth Eng 71(5):505–528

    Article  Google Scholar 

  • Yuan S, Wang Y, Xu J (2014) New progress in self-adaptive FEMOL analysis of 2D free vibration problems. Eng Mech 31(1):15–22 (In Chinese)

    Google Scholar 

  • Yuan S, Wang Y, Ye K (2013) An adaptive FEM for buckling analysis of non-uniform Bernoulli-Euler members via the element energy projection technique. Math Prob Eng, 1–6

    Google Scholar 

  • Yuan S, Ye K, Wang Y, Kennedy D, Williams FW (2017) Adaptive finite element method for eigensolutions of regular second and fourth order Sturm-Liouville problems via the element energy. Eng Comput 34(8):2862–2876

    Article  Google Scholar 

  • Zacharias J, Hartmann C, Delgado A (2004) Damage detection on crates of beverages by artificial neural networks trained with finite-element data. Comput Meth Appl Mech Eng 193(6–8):561–574

    Article  Google Scholar 

  • Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Butterworth-Heinemann, Oxford

    Google Scholar 

  • Zienkiewicz OC, Zhu J (1992a) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Num Meth Eng 33(7):1331–1364

    Google Scholar 

  • Zienkiewicz OC, Zhu J (1992b) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Num Meth Eng 33(7):1365–1382

    Google Scholar 

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Correspondence to Yongliang Wang .

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Wang, Y. (2021). Adaptive Finite Element Algorithm for Damage Detection of Non-Uniform Euler-Bernoulli Beams with Multiple Cracks Based on Natural Frequencies. In: Adaptive Analysis of Damage and Fracture in Rock with Multiphysical Fields Coupling. Springer, Singapore. https://doi.org/10.1007/978-981-15-7197-8_5

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