DOI QR코드

DOI QR Code

Dynamic responses of a beam with breathing cracks by precise integration method

  • Cui, C.C. (Department of Mechanics, Sun Yat-sen University) ;
  • He, X.S. (Department of Mechanics, Sun Yat-sen University) ;
  • Lu, Z.R. (Department of Mechanics, Sun Yat-sen University) ;
  • Chen, Y.M. (Department of Mechanics, Sun Yat-sen University) ;
  • Liu, J.K. (Department of Mechanics, Sun Yat-sen University)
  • 투고 : 2015.01.22
  • 심사 : 2016.10.06
  • 발행 : 2016.12.10

초록

The beam structure with breathing cracks subjected to harmonic excitations was modeled by FEM based on Euler-Bernoulli theory, and a piecewise dynamical system was deduced. The precise integration method (PIM) was employed to propose an algorithm for analyzing the dynamic responses of the deduced system. This system was first divided into linear sub-systems, between which there are switching points resulted from the breathing cracks. The inhomogeneous terms due to the external excitations were tackled by introducing auxiliary variables to express the harmonic functions, hence the sub-systems are homogeneous. The PIM was then applied to solve the homogeneous sub-systems one by one. During the procedures, a predictor-corrector algorithm was presented to determine the switching points accurately. The presented method can provide solutions with an accuracy to a magnitude of $10^{-12}$ compared with exact solutions obtained by the theories of ordinary differential equations. The PIM results are much more accurate than Newmark ones with the same time step. Moreover, it is found that the PIM can maintain a high level of accuracy even when the time step increases within a relatively wide range.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Abdel Wahab, M.M., De Roeck, G. and Peeters, B. (1999), "Parameterization of damage in reinforced concrete structures using model updating", J. Sound Vib., 228(4), 717-30. https://doi.org/10.1006/jsvi.1999.2448
  2. Akbas and Doguscan, S. (2016), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., 59 (3), 579-599. https://doi.org/10.12989/sem.2016.59.3.579
  3. Andreaus, U. and Baragatti, P. (2009), "Fatigue crack growth, free vibrations and breathing crack detection of Aluminium Alloy and Steel beams", J. Strain Analysis for Eng. Design, 44(7), 595-608. https://doi.org/10.1243/03093247JSA527
  4. Andreaus, U. and Baragatti, P. (2011), "Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response", J. Sound Vib., 330 (4), 721-742. https://doi.org/10.1016/j.jsv.2010.08.032
  5. Andreaus, U. and Baragatti, P., (2012), "Experimental damage detection of cracked beams by using nonlinear characteristics of forced response", Mech. Syst. Signal Process. 31(8), 382-404. https://doi.org/10.1016/j.ymssp.2012.04.007
  6. Andreaus, U., Batra, R.and Porfiri, M. (2005), "Vibrations of Cracked Euler-Bernoulli Beams using Meshless Local Petrov-Galerkin (MLPG) Method", Comput. Model. Eng. Sci. (CMES), 9(2), 111-131.
  7. Andreaus, U., Casini, P. and Vestroni, F. (2003), "Frequency reduction in elastic beams due to a stable crack: numerical results compared with measured test data", Eng. Trans., 51(1), 1-16.
  8. Andreaus, U., Casini, P. and Vestroni, F. (2005), "Nonlinear features in the dynamic response of a cracked beam under harmonic forcing", Proc. of DETC'05, 2005 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, California, USA, September.
  9. Andreaus, U., Casini, P. and Vestroni, F., (2007), "Nonlinear Dynamics of a Cracked Cantilever Beam Under Harmonic Excitation", Int. J. Nonlin. Mech., 42(3), 566-575. https://doi.org/10.1016/j.ijnonlinmec.2006.08.007
  10. Ariaei, A., Ziaei-Rad, S. and Ghayour, M. (2009), "Vibration analysis of beams with open and breathing cracks subjected to moving masses", J. Sound Vib., 326(3-5), 709-724. https://doi.org/10.1016/j.jsv.2009.05.013
  11. Bouboulas, A.S. and Anifantis, N.K. (2011), "Finite element modeling of a vibrating beam with a breathing crack: observations on crack detection", Struct. Health Monitoring, Int. J., 10(2), 131-145. https://doi.org/10.1177/1475921710373286
  12. Caddemi, S., Calio, I. and Marletta, M. (2010), "The non-linear dynamic response of the Euler-Bernoulli beam with an arbitrary number of switching cracks", Int. J. Non-linear Mech., 45(7), 714-726. https://doi.org/10.1016/j.ijnonlinmec.2010.05.001
  13. Chondros, T.G., Dimarogonas, A.D. and Yao, J. (2001), "Vibration of a beam with a breathing crack", J. Sound Vib., 239 (1), 57-67. https://doi.org/10.1006/jsvi.2000.3156
  14. Cui, C.C., Liu, J.K. and Chen, Y.M. (2015), "Simulating nonlinear aeroelastic responses of an airfoil with freeplay based on precise integration method", Commun. Nonlin. Sci. Numer. Simulat., 22, 933-942. https://doi.org/10.1016/j.cnsns.2014.08.002
  15. Gao, Q., Wu, F., Zhang, H.W., Zhong, W.X., Howson, W.P. and Williams, F.W. (2012), "A fast precise integration method for structural dynamics problems", Struct. Eng. Mech., 43(1), 1-13. https://doi.org/10.12989/sem.2012.43.1.001
  16. Gu, Y.X., Chen, B.S., Zhang, H.W. and Guan, Z.Q. (2001), "Precise time-integration method with dimensional expanding for structural dynamic equations", AIAA J., 39(12), 2394-2399. https://doi.org/10.2514/2.1248
  17. Hossein, A.M., Foad, N. and Soltani, R.J. (2014), "A multi-crack effects analysis and crack identification in functionally graded beams using particle swarm optimization algorithm and artificial neural network", Struct. Eng. Mech., 51(2), 299-313. https://doi.org/10.12989/sem.2014.51.2.299
  18. Huang, Y., Deng, Z.C. and Yao, L.X. (2007), "An improved symplectic precise integration method for analysis of the rotating rigid-flexible coupled system", J. Sound Vib., 299(1-2), 229-246. https://doi.org/10.1016/j.jsv.2006.07.009
  19. Jena, S.P., Parhi, D.R. and Mishra, D. (2015), "Comparative study on cracked beam with different types of cracks carrying moving mass", Struct. Eng. Mech., 56 (5), 797-811. https://doi.org/10.12989/sem.2015.56.5.797
  20. Kim, J.T. 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
  21. Kisa, K. and Brandon, J. (2000), "The effects of closure of cracks on the dynamics of a cracked cantilever beam", J. Sound Vib., 238 (1), 1-18. https://doi.org/10.1006/jsvi.2000.3099
  22. Kisa, M. (2012), "Vibration and stability of axially loaded cracked beams", Struct. Eng. Mech., 44(3), 305-323. https://doi.org/10.12989/sem.2012.44.3.305
  23. Krawczuk, M. (2002), "Application of spectral beam finite element with a crack and iterative search technique for damage detection", Finite Elements Anal. Design, 38(6), 537-548. https://doi.org/10.1016/S0168-874X(01)00084-1
  24. Law, S.S. and Zhu, X.Q. (2004), "Dynamic behavior of damaged concrete bridge structures under moving vehicular loads", Eng. Struct., 26(9), 1279-1293. https://doi.org/10.1016/j.engstruct.2004.04.007
  25. Lee, J. and Fenves, G.L. (1998), "Plastic-damage model for cyclic loading of concrete structures", J. Eng. Mech. ASCE, 124(8), 892-900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892)
  26. Lin, G., Han, Z.J., Zhong, H. And Li, J.B. (2013), "A precise integration approach for dynamic impedance of rigid strip footing on arbitrary anisotropic layered half-space", Soil Dyn. Earthquake Eng., 49, 96-108. https://doi.org/10.1016/j.soildyn.2013.01.009
  27. Moradi, S., Razi, P. and Fatahi, L. (2011), "On the application of bees algorithm to the problem of crack detection of beam-type structures", Comput. Struct., 89 (23-24), 2169-2175. https://doi.org/10.1016/j.compstruc.2011.08.020
  28. Ozkul, T.A. (2004), "A finite element formulation for dynamic analysis of shells of general shape by using the Wilson-$\theta$ method", Thin-Walled Struct., 42(4), 497-513. https://doi.org/10.1016/j.tws.2003.12.008
  29. Sinha, J.K., Friswell, M.I. and Edwards, S. (2002), "Simplified models for the location of cracks in beam structures using measured vibration data", J. Sound Vib., 251(1), 13-38. https://doi.org/10.1006/jsvi.2001.3978
  30. Wang, M.F. (2011), "Reduced-order precise integration methods for structural dynamic equations", Int. J. Numer. Meth. Biomed. Eng., 27(10), 1569-1582. https://doi.org/10.1002/cnm.1382
  31. Wang, W.J., Lu, Z.R. and Liu, J.K. (2012), "Time-frequency analysis of a coupled bridge-vehicle system with breathing cracks", Int. Multis. Mech., 5(3), 169-185. https://doi.org/10.12989/imm.2012.5.3.169
  32. Zhang, W.Z. and Huang, P.Y. (2013), "Precise integration method for a class of singular two-point boundary value problems", Acta Mech. Sin., 29(2), 233-240. https://doi.org/10.1007/s10409-013-0006-5
  33. Zhong,W.X. (2004), "On precise integration method", J. Comput. Appl. Math., 163(1), 59-78. https://doi.org/10.1016/j.cam.2003.08.053
  34. Zhong, W.X. and Williams, F.W. (1994), "A precise time step integration method", Proc. Inst. Mech. Eng., 208, 427-430.