Structural Engineering and Mechanics

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Free vibration of multi-cracked beams

  • Selmi, Abdellatif (College of Engineering, Department of Civil Engineering, Prince Sattam bin Abdulaziz University)
  • Received : 2020.05.26
  • Accepted : 2021.06.09
  • Published : 2021.08.25
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Abstract

A new method is presented to study the free vibrations of multi-cracked beams with arbitrary boundary conditions. In the literature, the method based on changes in modal strain energy was used to perform the dynamic analysis of beams with just one crack. In this paper, the changes in modal strain energy are used iteratively to study the dynamic behavior of beams with multiple cracks. The iterative method consists in finding the dynamic frequencies in steps by considering the effects of cracks one by one. First, the beam is assumed intact, for it a single crack is taken into account via the method based on changes in modal strain energy. Then, this procedure is repeated iteratively by taking at steps (i+1), the frequencies obtained at step (i). The end is detected when the total number of cracks is reached. This developed iterative approach is used to analyze the effect of multiple open cracks on the modal parameters of a cantilever beam subjected to free vibration. The results are in good agreement with finite element and experimental methods. This developed method may also be used to generate training data for pattern recognition approaches to health monitoring.

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References

  1. Akbas, S.D. (2019), "Nonlinear behavior of fiber reinforced cracked composite beams", Steel Compos. Struct., 30(4), 327-326. https://doi.org/10.12989/scs.2019.30.4.327.
  2. Aleyaasin, M., Ebrahimi, M. and Whalley, R. (2001), "Vibration analysis of distributed-lumped rotor systems", Comput. Meth. Appl. Mech. Eng., 189, 545-558. https://doi.org/10.1016/s0045-7825(99)00308-4.
  3. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  4. Anderson, T.L. (2005), Fracture Mechanics: Fundamental and Applications, Third Edition, CRC Press. Taylor and Francis Group, London.
  5. Benzair, A., Maachou, M., Amara, K.H. and Tounsi, A. (2006), "Effect of transverse cracks on the elastic properties of high temperature angle-ply laminated composites", Comput. Mater. Sci., 37(4), 470-475. https://doi.org/10.1016/j.commatsci.2005.11.006.
  6. Bilello, C. and Bergman, L.A. (2004), "Vibration of damaged beams under a moving mass: theory and experimental validation", J. Sound Vib., 274, 567-582. https://doi.org/10.1016/j.jsv.2003.01.001.
  7. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Bedia, E.A.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166. https://doi.org/10.12989/cac.2020.25.2.155.
  8. Caddemi, S. and Morassi, A. (2013), "Multi-cracked eulerbernoulli beams: mathematical modeling and exact solution", Int. J. Solid. Struct., 50, 944-956. https://doi.org/10.1016/j.ijsolstr.2012.11.018.
  9. Caddemi, S., Calio, I., Cannizzaro, F. and Rapicavoli, D. (2013), "A novel beam finite element with singularities for the dynamic analysis of discontinuous frames", Arch. Appl. Mech., 83(10), 1451-1468. https://doi.org/10.1007/s00419-013-0757-2.
  10. Chen, L.H., Duan, J.W., Sun, Y. and Li, J. (2013), "The study of the vibration characteristics of the cantilever beam with a surface crack", Appl. Mech. Mater., 394(C), 121-127. https://doi.org/10.4028/www.scientific.net/AMM.394.121.
  11. Chondros, T.G., Dimarogonas, A.D. and Yao, J.A. (1998), "A continuous cracked beam vibration theory", J. Sound Vib., 215(1), 17-34. https://doi.org/10.1006/jsvi.1998.1640.
  12. Christides, S. and Barr, A.D.S. (1984), "One-dimensional theory of cracked bernoulli-euler beams", Int. J. Mech. Sci., 26, 639-648. https://doi.org/10.1016/0020-7403(84)90017-1.
  13. Cunedioglu, Y. (2015), "Free vibration analysis of edge cracked symmetric functionally graded sandwich beams", Struct. Eng. Mech., 56(6), 1003-1020. https://doi.org/10.12989/sem.2015.56.6.1003.
  14. Dimarogonas, A.D. and Paipetis S.A. (1983), Analytical Methods in Rotor Dynamics, Applied Science Publisher, London.
  15. El Meiche, N., Tounsi, A. and Megueni, A. (2009), "Analysis of the transverse cracking in hybrid cross-ply composite laminates", Comput. Mater. Sci., 46(4), 1102-1108 https://doi.org/10.1016/j.commatsci.2009.05.019.
  16. Gudmundson, P. (1982), "Eigenfrequency changes of structures due to cracks, notches or other geometrical changes", J. Mech. Phys. Solid., 30(5), 339-353. https://doi.org/10.1016/0022-5096(82)90004-7.
  17. Guojin, T., Jinghui, S., Chunli, W. and Wensheng, W. (2017), "Free vibration analysis of cracked Timoshenko beams carrying spring-mass systems", Struct. Eng. Mech., 63(4), 551-565. https://doi.org/10.12989/SEM.2017.63.4.551.
  18. Habibullah, B., Emre, D. and Fehim, F. (2019), "Effect of fatigue crack propagation on natural frequencies of system in AISI 4140 Steel", Steel Compos. Struct., 32(3), 305-312. https://doi.org 10.12989/scs.2019.32.3.305.
  19. Huang, M., Lei, Y. and Cheng, S. (2019), "Damage identification of bridge structure considering temperature variations based on particle swarm optimization-cuckoo search algorithm", Mech. Syst. Signal Pr., 115, 361-379. https://doi.org/10.1177/1369433219861728.
  20. Hussain, M., Naeem, M.N., Khan, M.S. and Tounsi, A. (2020b). "Computer-aided approach for modelling of FG cylindrical shell sandwich with ring supports", Comput. Concrete, 25(5), 411-425. https://doi.org/10.12989/cac.2020.25.5.411.
  21. Hussain, M., Naeem, M.N., Taj, M. and Tounsi, A. (2020a), "Simulating vibration of single-walled carbon nanotube using Rayleigh-Ritz's method", Adv. Nano Res., 8(3), 215-228. https://doi.org/10.12989/ANR.2020.8.3.215.
  22. Ibrahim, A.M., Ozturk, H. and Sabuncu, M. (2013), "Vibration analysis of cracked frame structures", Struct. Eng. Mech., 45(1), 33-52. https://doi.org/10.12989/sem.2013.45.1.033.
  23. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/CAC.2020.25.1.037.
  24. Karami, B., Janghorban, M. and Tounsi, A. (2019), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  25. Khatir, S. and Abdel-Wahab, M. (2018), "Fast simulations for solving fracture mechanics inverse problems using POD-RBF XIGA and Jaya algorithm", Eng. Fract. Mech., 205, 285-300. https://doi.org/10.1016/j.engfracmech.2018.09.032.
  26. Khatir, S., Abdel-Wahab, M., Boutchicha, D. and Khatir, T. (2019), "Structural health monitoring using modal strain energy damage indicator coupled with teaching-learning-based optimization algorithm and isogoemetric analysis", J. Sound Vib., 448, 230-246. https://doi.org/10.1016/j.jsv.2019.02.017.
  27. Khatir, S., Boutchicha, D., Le Thanh, C., Tran-Ngoc, H., Nguyen, T.N. and Abdel-Wahab, M. (2020a), "Improved ANN technique combined with Jaya algorithm for crack identification in plates using XIGA and experimental analysis", Theor. Appl. Fract. Mech., 107, 102554. https://doi.org/10.1016/j.tafmec.2020.102554.
  28. Khatir, S., Khatir, T., Boutchicha, D., Le Thanh, C., Tran, H., Bui, T.Q., ... & Abdel Wahab, M. (2020b), "An efficient hybrid TLBO-PSO-ANN for fast damage identification in steel beam structures using IGA", Smart Struct Syst., 25(5), 605-617. http://doi.org/10.12989/sss.2020. 25.5.605.
  29. Khiem, N.T. and Lien, T.V. (2001), "A simplified method for natural frequency analysis of a multiple cracked beam", J. Sound Vib., 245(4), 737-751. https://doi.org/10.1006/jsvi.2001.3585.
  30. Kim, J. and Stubbs, N. (2003), "Crack detection in beam-type structures using frequency data", J. Sound Vib., 259(1), 145-160. https://doi.org/10.1006/jsvi.2002.5132.
  31. Kisa, M. and Arif, G. (2006), "Modal analysis of multi-cracked beams with circular cross section", Eng. Fract. Mech., 73, 963-977. https://doi.org/10.1016/j.engfracmech.2006.01.002.
  32. Kisa, M., Brandon, J. and Topcu, M. (1998), "Free Vibrational Analysis of Cracked beams by combination of finite elements and component mode synthesis method", Comput. Struct., 67, 215-223. https://doi.org/10.1016/S0045-7949(98)00056-X.
  33. Lee, J. (2009a), "Identification of multiple cracks in a beam using vibration amplitudes", J. Sound Vib., 326, 205-212. https://doi.org/10.1016/j.jsv.2009.04.042.
  34. Lee, J. (2009b), "Identification of multiple cracks in a beam using natural frequencies", J. Sound Vib., 320, 482-490. https://doi.org/10.1016/j.jsv.2008.10.033.
  35. Lele, S.P. and Maiti, S.K. (2002), "Modeling of transverse vibration of short beams for crack detection and measurement of crack extension", J. Sound Vib., 257, 559-583. https://doi.org/10.1006/jsvi.2002.5059.
  36. Liu, W.H. and Huang, C.C. (1988), "Vibrations of a constrained beam carrying a heavy tip body", J. Sound Vib., 123, 15-29. https://doi.org/10.1016/S0022-460X(88)80074-9.
  37. Loya, J.A., Rubio, L. and Fernandez-Saez, J. (2006), "Natural frequencies for bending vibrations of Timoshenko cracked beams", J. Sound Vib., 29, 640-653. https://doi.org/10.1016/j.jsv.2005.04.005.
  38. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E.A.A., Tounsi, A. and Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.
  39. Mehrjoo, M., Khaji, N. and Ghafory-Ashtiany, M. (2013), "Application of genetic algorithm in crack detection of beam-like structures using a new cracked euler-bernoulli beam element", Appl. Soft Comput., 13, 867-880. https://doi.org/10.1016/j.asoc.2012.09.014.
  40. Mehrjoo, M., Khaji, N. and Ghafory-Ashtiany, M. (2014), "New timoshenko-cracked beam element and crack detection in beam-like structures using genetic algorithm", Invers. Prob. Sci. Eng., 22(3), 359-382. https://doi.org/10.1080/17415977.2013.788170.
  41. Morassi, A. (1993), "Crack-induced changes in eigenfrequeices of beam structures", J. Eng. Mech., 119, 1768-1803. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:9(1798).
  42. Mostafa, A. (2012), "A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions", Int. J. Mech. Sci., 57, 19-33. https://doi.org/10.1016/j.ijmecsci.2012.01.010.
  43. Narkis, Y. and Elmalah, E. (1996), "Crack identification in a cantilever beam under uncertain end conditions", Int. J. Mech. Sci., 38(6), 499-507. https://doi.org/10.1016/0020-7403(95)00071-2.
  44. Pestel, E.C. and Leckie, F.A. (1983), Matrix Methods in Elastomechanics, McGraw-ill, London.
  45. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A.A., Benrahou, K.H. and Tounsi, A. (2020). "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  46. Rizos, P.F., Aspragathos, N. and Dimarogonas, A.D. (1990), "Identification of crack location and magnitude in a cantilever beam from the vibration modes", J. Sound Vib., 138(3), 381-388. https://doi.org/10.1016/0022-460X(90)90593-O.
  47. Ruotolo, R. and Surace, C. (1997), "Damage assessment of multiple cracked beams: numerical results and experimental validation", J. Sound Vib., 206(4), 567-588. https://doi.org/10.1006/jsvi.1997.1109.
  48. Ruotolo, R. and Surace, C. (2004), "Natural frequencies of a bar with multiple cracks", J. Sound Vib., 272, 301-316. https://doi.org/10.1016/S0022-460X(03)00761-2.
  49. Sandeep, C., Umesh, P. and Nagpal, A.K. (2007), "An analytical-numerical procedure for cracking and time-dependent effects in continuous composite beams under service load", Steel Compos. Struct., 7(3), 219-240. https://doi.org/10.12989/scs.2007.7.3.219.
  50. Shen, M.H. and Pierre, C. (1986), "Modes of free vibrations of cracked beams", 1-46.
  51. Shen, M.H.H. and Pierre, C. (1994), "Free Vibrations of beams with a single-edge crack", J. Sound. Vib., 170(2), 237-259. https://doi.org/10.1006/jsvi.1994.1058.
  52. Shifrin, E.I. and Rutolo, R. (1999), "Natural frequencies of a beam with an arbitrary number of cracks", J. Sound. Vib., 222(3), 409-423. https://doi.org/10.1006/jsvi.1998.2083.
  53. Takahashi, I. (1999), "Vibration and stability of non-uniform cracked Timoshenkobeam subjected to follower force", Comput. Struct., 71, 585-591. https://doi.org/10.1016/S0045-7949(98)00233-8.
  54. Tounsi, A., Amara, K.H., Benzair, A. and Megueni, A. (2006), "On the transverse cracking and stiffness degradation of aged angle-ply laminates", Mater. Lett., 60(21-22), 2561-2564. https://doi.org/10.1016/j.matlet.2006.01.037.
  55. Tran-Ngoc, H., Khatir, S., Le-Xuan, T., De Roeck, G., Bui-Tien, T. and Abdel-Wahab, M. (2020), "A novel machine-learning based on the global search techniques using vectorized data for damage detection in structures", Int. J. Eng. Sci., 157, 103376. https://doi.org/10.1016/j.ijengsci.2020.103376.
  56. Ugurcan, E. and Ekrem, T. (2016), "Exact solution based finite element formulation of cracked beams for crack detection", Int. J. Solid. Struct., 96, 240-253. https://doi.org/10.1016/j.ijsolstr.2016.06.005.
  57. Xiang, J., Zhong, Y., Chen, X. and He, Z. (2008), "Crack detection in a shaft by combination of wavelet-based elements and genetic algorithm", Int. J. Solid. Struct., 45, 4782-4795. https://doi.org/10.1016/j.ijsolstr.2008.04.014.
  58. Yang, L and Dong, W.S. (2015), "Effects of edge crack on the vibration characteristics of delaminated beams", Struct. Eng. Mech., 53(4), 767-780. https://doi.org/10.12989/sem.2015.53.4.767.
  59. Zheng, D.Y. and Fan, S.C. (2003), "Vibration and stability of cracked hollow-sectional beams", J. Sound. Vib., 267, 933-954. https://doi.org/10.1016/S0022-460X(02)01605-X.