Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Modal analysis of cracked cantilever composite beams

  • Kisa, Murat (Mechanical Engineering Department, Faculty of Engineering, Harran University) ;
  • Arif Gurel, M. (Civil Engineering Department, Faculty of Engineering, Harran University)
  • Received : 2003.10.15
  • Accepted : 2005.03.07
  • Published : 2005.05.30
⟨ Previous Next ⟩

Abstract

Modal analysis of cracked cantilever composite beams, made of graphite-fibre reinforced polyamide, is studied. By using the finite element and component mode synthesis methods, a numeric model applicable to investigate the vibration of cracked composite beams is developed. In this new approach, from the crack section, the composite beam separated into two parts coupled by a flexibility matrix taking into account the interaction forces. These forces are derived from the fracture mechanics theory as the inverse of the compliance matrix calculated with the proper stress intensity factors and strain energy release rate expressions. Numerical results are obtained for modal analysis of composite beams with a transverse non-propagating open crack, addressing the effects of the location and depth of the crack, and the volume fraction and orientation of the fibre on the natural frequencies and mode shapes. By means of modal data, the position and dimension of the defect can be found. The results of the study confirmed that presented method is suitable for the vibration analysis of cracked cantilever composite beams. Present technique can be easily extended to composite plates and shells.

Keywords

References

  1. Adams, R.D., Cawley, P., Pye, C.J. and Stone, J. (1978), 'A vibration testing for non-destructively assessing the integrity of the structures', J. Mech. Eng. Sci., 20, 93-100 https://doi.org/10.1243/JMES_JOUR_1978_020_016_02
  2. Bao, G, Ho, S., Suo, Z. and Fan, B. (1992), 'The role of material orthotropy in fracture specimens for composites', Int. J. Solids Struct., 29, 1105-1116 https://doi.org/10.1016/0020-7683(92)90138-J
  3. Cawley, P. and Adams, R.D. (1979), 'The location of defects in structures from measurements of natural frequencies', J. Strain Analysis, 14, 49-57 https://doi.org/10.1243/03093247V142049
  4. Dimarogonas, A.D. (1996), 'Vibration of cracked structures: A state of the art review', Eng. Fract. Mech., 55(5), 831-857 https://doi.org/10.1016/0013-7944(94)00175-8
  5. Gouranis, G. and Dimarogonas, A.D. (1988), 'A finite element of a cracked prismatic beam for structural analysis', Comput. Struct., 28, 309-313 https://doi.org/10.1016/0045-7949(88)90070-3
  6. Hurty, W.C. (1965), 'Dynamic analysis of structures using substructure modes', AIAA J., 3, 678-685 https://doi.org/10.2514/3.2947
  7. Kisa, M., Brandon, J.A. and Topcu, M. (1998), 'Free vibration analysis of cracked beams by a combination of finite elements and component mode synthesis methods', Comput. Struct., 67(4), 215-223 https://doi.org/10.1016/S0045-7949(98)00056-X
  8. Kisa, M. and Brandon, J.A. (2000a), 'Free vibration analysis of multiple open-edge cracked beams by component mode synthesis', Struct. Eng. Mech., 10(1), 81-92 https://doi.org/10.12989/sem.2000.10.1.081
  9. Kisa, M. and Brandon, J.A. (2000b), '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
  10. Krawczuk, M., Ostachowicz, W. and Zak, A. (1997), 'Modal analysis of cracked, unidirectional composite beam', Composites Part B, 28B, 641-650
  11. Krawczuk, M. and Ostachowicz, W.M. (1995), 'Modelling and vibration analysis of a cantilever composite beam with a transverse open crack', J. Sound Vib., 183(1), 69-89 https://doi.org/10.1006/jsvi.1995.0239
  12. Krawczuk, M. (1994), 'A new finite element for the static and dynamic analysis of cracked composite beams', Comput. Struct., 52(3), 551-561 https://doi.org/10.1016/0045-7949(94)90240-2
  13. Nikpour, K. and Dimarogonas, A.D. (1988), 'Local compliance of composite cracked bodies'. Compos. Sci. Technol., 32, 209-223 https://doi.org/10.1016/0266-3538(88)90021-8
  14. Nikpour, K. (1990), 'Buckling of cracked composite columns', Int. J. Solids Struct., 26(12), 1371-1386 https://doi.org/10.1016/0020-7683(90)90084-9
  15. Oral, S. (1991), 'A shear flexible finite element for non-uniform laminated composite beams', Comput. Struct., 38(3), 353-360 https://doi.org/10.1016/0045-7949(91)90112-Y
  16. Przemieniecki, J.S. (1967), Theory of Matrix Structural Analysis, London, McGraw-Hill, first edition
  17. Ruotolo, R., Surace, C., Crespo, P. and Storer, D. (1996), 'Harmonic analysis of the vibrations of a cantilevered beam with a closing crack', Comput. Struct., 61, 1057-1074 https://doi.org/10.1016/0045-7949(96)00184-8
  18. Shen, M.H.H. and Chu, Y.C. (1992), 'Vibrations of beams with a fatigue crack', Comput. Struct., 45, 79-93 https://doi.org/10.1016/0045-7949(92)90347-3
  19. Song, O., Ha, T.W. and Librescu, L. (2003), 'Dynamics of anisotropic composite cantilevers weakened by multiple transverse open cracks', Eng. Fract. Mech., 70, 105-123 https://doi.org/10.1016/S0013-7944(02)00022-X
  20. Tada, H., Paris, P.C. and Irwin, G.R. (1985), The Stress Analysis of Cracks Handbook, St. Louis, Missouri 63105, Paris production incorporated and Del Research Corporation, Second edition
  21. Vinson, J.R. and Sierakowski, R.L. (1991), Behaviour of Structures Composed of Composite Materials, Dordrecht, Martinus Nijhoff, first edition
  22. Wauer, J. (1991), 'Dynamics of cracked rotors: a literature survey', Applied Mechanics Reviews, 17, 1-7

Cited by

  1. An improved modal strain energy method for structural damage detection, 2D simulation vol.54, pp.1, 2015, https://doi.org/10.12989/sem.2015.54.1.105
  2. Effects of edge crack on the vibration characteristics of delaminated beams vol.53, pp.4, 2015, https://doi.org/10.12989/sem.2015.53.4.767
  3. Dynamic stiffness matrix of composite box beams vol.9, pp.5, 2005, https://doi.org/10.12989/scs.2009.9.5.473
  4. Free-vibration analysis of cracked beam with constant width and linearly varying thickness vol.11, pp.1, 2005, https://doi.org/10.1680/jemmr.21.00015a