전달행렬법을 사용하여 균열이 있는 티모센코 보의 동특성 해석

Kim, Jung Ho;Kwak, Jong Hoon;Lee, Jung Woo;Lee, Jung Youn

  • 투고 : 2016.01.18
  • 심사 : 2016.04.05
  • 발행 : 2016.04.20


This paper presents a numerical method that can evaluate the effect of crack for the in-plane bending vibration of Timoshenko beam. The method is a transfer matrix method that the element transfer matrix is deduced from the element dynamic stiffness matrix. An edge crack is expressed as a rotational spring, and then is formulated as an independent transfer matrix. To demonstrate the accuracy of this theory, the results computed from the present are compared with those obtained from the commercial finite element analysis program. Based on these comparison results, a parametric study is performed to analyze the effects for the size and locations of crack.


균열;동강성 행렬;유한요소법;전달행렬법;티모센코 보;동특성


  1. Krawczuk, M., 1994, Coupled Logitudinal and Bending Forced Vibration of Timoshenko Cantilever Beam with a Close Crack, Journal of Theoretical and Applied Mechanics, Vol. 2, No. 32, pp. 463~482.
  2. Fan, W. and Qiao, P., 2011, Vibration-based Damage Identification Methods: A Review and Comparative Study, Structural Health Monitoring, Vol. 10, No. 1, pp. 83~111.
  3. Hur, Y-C., Kim, J.-K. and Park, S.-H., 2007, A Study about the Damage Model of a Cantilever Beam with Open Crack Generated in Whole Breadth of the Beam, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 17, No. 10, pp. 936~945.
  4. Balasubramanian, K. R., Sivapirakasam, S. P. and Anand, R., 2014, Vibration Analysis of a Timoshenko Beam with Transverse Open Crack by Finite Element Method, Applied Mechanics & Materials, Vol. 592-594, pp. 2102~2106.
  5. Kisa, M., Brandon, J. and Topcu, M., 1998, Free Vibration Analysis of Cracked beams By a Combination of Finite Elements and Component Mode Synthesis Methods, Computers and Structures, Vol. 67, pp. 215~223.
  6. Bui, N. N., Ngo, M., Nikolic, M., Brancherie, D. and Ibrahimbegovic, A., 2014, Enriched Timoshenko Beam Finite Element for Modeling Bending and Shear Failure of Reinforced Concrete Frames, Computers and Structures, Vol. 143, pp. 9~18.
  7. Wu, J. and Chen, C., 2007, A Lumped-mass TMM for Free Vibration Analysis of a Multi-step Timoshenko Beam Carrying Eccentric Lumped Masses with Rotary Inertias, Journal of Sound and Vibration, Vol. 301, No. 3-5, pp. 878~897.
  8. Nandakumar, P. and Shankar, K., 2015, Structural Crack Damage Detection Using Transfer Matrix and State Vector, Measurement, Vol. 68, pp. 310~327.
  9. Carneiro, S. H. S. and Inman, D. J., 2002, Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams, Journal of Vibration and Acoustics, Vol. 124, No. 2, pp. 310~320.
  10. Attar, M., Karrech, A. and Regenauer-Lieb, K., 2014, 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, pp. 2359~2377.
  11. Sasmal, S. and Ramanjaneyulu, K., 2009, Detection and Quantification of Structural Damage of a Beam-like Structure Using Natural Frequencies, Engineering, Vol. 1, pp. 167~176.
  12. Heydari, M. and Ebrahimi, A., 2015, Continuous Model for Flexural Vibration Analysis of Timoshenko Beams with a Vertical Edge Crack, Archive of Applied Mechanics, Vol. 85, No. 5, pp. 601~615.
  13. Rakideh, M., Dardel, M. and Pashaei, M. H., 2013, Crack Detection of Timoshenko Beams Using Vibration Behavior and Neural Network, International Journal of Engineering, Vol. 26, No. 12, pp. 1433~1444.
  14. Swamidas, A. S. J., Yang, X. and Seshadri, R., 2004, Identification of Cracking in Beam Structures Using Timoshenko and Euler Formulations, Journal of Engineering Mechanics, Vol. 11, No. 11, pp. 1297~1308.
  15. Gounaris, G. and Dimagoronas, A. D., 1988, A Finite Element of a Cracked Prismatic Beam for Structural Analysis, Computers and Structures, Vol. 28, No. 1, pp. 309~313.
  16. Noll, S., Dreyer, J. T. and Singh, R., 2013, Identification of Dynamic Stiffness Matrices of Elastomeric Joints Using Direct and Inverse Methods, Mechanical Systems and Signal Processing, Vol. 39, No. 1-2, pp. 227~244.


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