Dynamic Response of Multi-cracked Beams Resting on Elastic Foundation

Authors

University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

Cracks cause to change dynamic response of beams and make discontinuity in slope of the deflection of the beams. The dynamic analysis of the Euler-Bernoulli cracked beam on the elastic foundation subjected to the concentrated load is presented in this paper. The stiffness of the elastic foundation and elastic supports influence on vibrational characteristics of the cracked beam. The Dynamic Green Function is applied to solve the governing equation. Thus, the dynamic response of the cracked beam is determined by Laplace Transform method. The effects of depth and location of the crack on natural frequency and deflection of the cracked beam on an elastic foundation are evaluated. In order to demonstrate the capability of the present approach, several numerical examples are worked out and the results are discussed.

Keywords


  1. Bovsunovsky, A. P., Matveev, V. V. "Analytical approach to the determination of dynamic characteristics of a beam with a closing crack", Journal of Sound and Vibration, Vol 235, No. 3, (2000), 415-434.
  2. Khiem, N. T., Lien, T. V. A. "Simplified method for natural frequency analysis of a multiple cracked beam", Journal of Sound and Vibration, Vol 245, No. 4, (2001), 737-751.
  3. Qiang, J., Furman, M. A., Ryne, R. D. "Strong-strong beam-beam simulation using a Green function approach", Physical Review Special Topics-Accelerators and Beams, Vol 5, No. 10, (2002), 104402.
  4. Kim, J. T., and Stubbs, N. "Crack detection in beam-type structures using frequency data", Journal of Sound and Vibration, Vol 259, No. 1, (2003), 145-160.
  5. Khnaijar, A., and Benamar, R., "A discrete model for nonlinear vibrations of a simply supported cracked beams resting on elastic foundations", Diagnostyka, Vol. 18, No. 3, (2017), 39-46.
  6. Chang, C. C., Chen, L. W, "Detection of the location and size of cracks in the multiple cracked beam by spatial wavelet based approach", Mechanical Systems and Signal Processing, Vol. 1, No. 1, (2005), 139-155.
  7. Xiang, J. W., Chen, X. F., Li, B., He, Y. M., He, Z. J, "Identification of a crack in a beam based on the finite element method of a B-spline wavelet on the interval", Journal of Sound and Vibration, Vol 296, No. 4, (2006), 1046-1052.
  8. Yoon, H. I., Son, I. S., Ahn, S. J, "Free vibration analysis of Euler-Bernoulli beam with double cracks", Journal of Mechanical Science and Technology, Vol 21, No3, (2007), 476-485.
  9. Sekhar, A. S. "Multiple cracks effects and identification", Mechanical Systems and Signal Processing, Vol. 22, No. 4, (2008), 845-878.
  10. Xiaoqing, Z., Qiang, H., Feng, L, "Analytical approach for detection of multiple cracks in a beam", Journal of Engineering Mechanics, Vol 136, No. 3, (2010), 345-357.
  11. Deokar, A. V., Wakchaure, V. D. "Experimental Investigation of Crack Detection in Cantilever Beam Using Natural Frequency as Basic Criterion", Institute of Technology, Nirma University, Ahmedabad, (2011).
  12. Attar, M., Karrech, A., andRegenauer-Lieb, K., "Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice spring model", Journal of Sound and Vibration, Vol. 333 No. 11, (2014), 2359-2377.
  1. Kural, S., Özkaya, E., "Size-dependent vibrations of a micro beam conveying fluid and resting on an elastic foundation", Journal of Vibration and Control, Vol. 23 No. 7, (2017), 1106-1114.
  2. Batihan, A. Ç., andKadioğlu, F. S., "Vibration analysis of a cracked beam on an elastic foundation", International Journal of Structural Stability and Dynamics, Vol. 16 No. 5, (2016), 1550006.
  3. TadiBeni, Y., Jafaria, A., andRazavi, H, "Size effect on free transverse vibration of cracked nano-beams using couple stress theory", International, Journal of Engineering, Transactions B: Applications, Vol. 28, No. 2, (2015), 296-304
  4. Sadeghian, M., EkhteraeiToussi, H., "Frequency analysis for a timoshenko beam located on an elastic foundation", Journal of Engineering, Transactions A: Basics, Vol. 24, No. 1, (2011), 87-105
  5. Ranjbaran, A., Hashemi, S., Ghaffarian, A. R., "A new approach for buckling and vibration analysis of cracked column", Journal of Engineering, Transactions A: Basics, Vol. 21, No. 3, (2008), 225-230
  6. Sherafatnia, K., Farrahi, G. H., Faghidian, S. A., "Analytic approach to free vibration and buckling analysis of functionally graded beams with edge cracks using four engineering beam theories", International. Journal of Engineering, Transactions C: Aspects, Vol. 27, No. 6, (2014), 979-990
  7. Nakhaei, A., Dardel, M., Ghasemi, M., andPashaei, M. (2014), "A simple method for modeling open cracked beam", International Journal of Engineering-Transactions B: Applications, 28(2), 321-329.
  8. Zhao, X., Zhao, Y. R., Gao, X. Z., Li, X. Y., Li, Y. H, "Green's functions for the forced vibrations of cracked Euler–Bernoulli beams", Mechanical Systems and Signal Processing, Vol 68, (2016), 155-175.
  9. Ghannadiasl, A., Mofid, M,"An analytical solution for free vibration of elastically restrained Timoshenko beam on an arbitrary variable Winkler foundation and under axial load", Latin American Journal of Solids and Structures, Vol. 12, No. 13, (2015), 2417-2438.
  10. Ghannadiasl, A., Mofid, M, "Dynamic Green function for response of Timoshenko beam with arbitrary boundary conditions", Mechanics Based Design of Structures and Machines, Vol. 42, No. 1, (2014), 97-110.
  11. Abu-Hilal, M., "Forced vibration of Euler–Bernoulli beams by means of dynamic Green functions", Journal of Sound and Vibration, Vol 267, No. 2, (2003), 191-207.
  12. Fernandez-Saez, J., Rubio, L., Navarro, C, "Approximate calculation of the fundamental frequency for bending vibrations of cracked beams", Journal of Sound and Vibration, Vol 225, No. 2, (1999), 345-352.
  13. Bilello, C. "Theoretical and experimental investigation on damaged beams under moving systems" (Doctoral dissertation, Ph. D. Thesis, Universitadegli Studi di Palermo, Italy, (2001).