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Frequency reduction in elastic beams due to a stable crack: numerical results compared with measured test data

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The presence of a crack could not only cause a local variation in the stiffness, but it could affect the mechanical behaviour of the entire structure to a considerable extent. The frequencies of natural vibrations, amplitudes of forced vibrations and areas of dynamic stability change due to the existence of such cracks. The vibration characteristics of cracked structures can be useful for non-destructive testing. In particular, the natural frequencies and mode shapes of cracked beams can provide insight into the extent of damage. The beam has been schematized as a 2-D continuous medium and discretized by means of quadrilateral finite elements. The lowest three natural frequencies (and the associated mode shapes) of the cracked cantilever beam, were obtained via both the modal and spectral analyses, and were compared with experimental data from literature in order to assess the reliability of different models of crack state, namely open crack and contact crack. Both the experimental and numerical results reveal the significant influence of the opening and closing conditions of the crack on the frequency reduction; namely this reduction decreases as more realistic contact phenomena are considered at crack interfaces.
Słowa kluczowe
EN
crack   beam  
PL
Rocznik
Strony
81--101
Opis fizyczny
Bibliogr. 24 poz., rys., tab.
Twórcy
autor
autor
autor
  • Dipartimento di Ingeneria Strutturale e Geotecnica, Universita degli Studi di Roma 'La Sapienza', 18 Via Eudossiana, 00184 Roma, Italy, paul.casini@uniroma1.it
Bibliografia
  • 1. O.N.L. ABRAHAM, J.A. BRANDON, The modelling of the opening and closing of a crack, ASME J. of Vibration, Acoustics, Stress and Reliability in Design, 117, 370–377, 1995.
  • 2. K.J. BATHE, Finite element procedures, Prentice Hali, Upper Saddle River, New Jersey, 1996.
  • 3. T.G. CHONDROS and A.D. DIMARONOGAS, Vibration of a cracked cantilever beam, Transaction of the ASME, 120, 742–746, 1998.
  • 4. T.G. CHONDROS, A.D. DIMAROGONAS, J. YAO, Vibration of a beam with a breathing crack, J. of Sound and Vibration, 239, l, 57–67, 2001.
  • 5. S. CHRISTIDES, A.D.S. BARR, One-dimensional theory of cracked Bernoulli-Euler beams, International Journal of Mechanic Science, 26, 11/12, 639–648, 1983.
  • 6. L.A. DIMAROGONAS, Vibration of cracked structures – A state of the art review, Eng. Fract. Mech., 55, 831–857, 1996.
  • 7. M.I. FRISWELL, J.E.T. PENNY, A simple nonlinear model of a cracked beam, Proc. of the 10"1 Int. Modal Analysis Conf., 516–521, California, San Diego 1992.
  • 8. G. GOUNARIS, A. DIMAROGONAS, A finite element of a cracked prismatic beam for structural analysis, Computers & Structures, 28, 3, 309–313, 1988.
  • 9. P. GUDMUNDSON, The dynamic behaviour of slender structures with cross-sectional cracks, J. Mech. Phys. Solids, 31, 4, 329–345, 1983.
  • 10. A. IBRAHIM, F. ISMAIL, and H.R. MARTIN, Modelling of the dynamics of a continuous beam including nonlinear fatigue crack, International Journal of Analytical and Experimental Modal Analysis, 2, 2, 76–82, 1987.
  • 11. T.Y. KAM, T.Y. LEE, Detection of cracks in structures using modal test data, Eng. Fract. Mech., 42, 2, 381–387, 1992.
  • 12. M. KISA, J. BRANDON, The effects of closure of cracks on the dynamics of a cracker cantilever beam, J. of Sound and Vibration, 238, l, 1–18, 2000.
  • 13. P. LÖTSTEDT, Coulomb friction in two-dimensional rigid body systems, ZAMM, 61, 605–615, 1981.
  • 14. C.A. PAPADOPOLOUS, A.D. DIMARONOGAS, Coupled longitudinal and bending vibrations of a rotating shaft with an open crack, Journal of Sound and Vibration, 117, 1, 81–93, 1987.
  • 15. G.L. QIAN, S.N. GU, J.S. JIANG, The dynamic behaviour and crack detection of a beam with a crack, Journal of Sound and Vibration, 138, 2, 233–243, 1990.
  • 16. A. RIVOLA, P.R. WHITE, Bispectral analysis of the bilinear oscillator with application to the detection of fatigue cracks, Journal of Sound and Vibration, 216, 5, 889–910, 1998.
  • 17. P.F. RIZOS, N. ASPRAGATHOS, A.D. DIMAROGONAS, Identification of crack location and magnitude in a cantilever beam from the vibration modes, Journal of Sound and Vibration, 138, 3, 381–388, 1990.
  • 18. R. RUOTOLO, C. SURACE, P. CRESPO, D. STORER, Harmonic analysis of the vibrations of a cantilevered beam with a closing crack, Computers fc Structures, 61, 6, 1057–1074, 1996.
  • 19. M.H.H. SHEN, Y.C. CHU, Vibrations of a beam with a fatigue crack, Computers & Structures, 45, l, 79–93, 1992.
  • 20. A. SIGNORINI, Lezioni di fisica matematica (in Italian), E.Y. VESCHI [Ed.], Rome 1951.
  • 21. J.K. SINHA, M.L FRISWELL, S. EDWARDS, Simplified models for the location of cracks in beam structures using measured vibration data, Journal of Sound and Vibration, 251, l, 13–38, 2002.
  • 22. H. TADA, P.C. PARIS, G.M. IRWIN, The stress analysis of cracks handbook, Asme Press, New York 2000.
  • 23. F. VESTRONI, D. CAPECCHI, Damage detection in beam structures based on frequency measurements, J. Mech. Eng. ASCE, 126, 7, 761–768, 2000.
  • 24. B. ZASTRAU, Vibrations of cracked structures, Arch. Mech., 37, 731–743, 1985.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0007-0018
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