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Dynamic analysis of a cracked bar by the method of characteristics

Dynamic analysis of a cracked bar by the method of characteristics The purpose of this paper is to introduce a new numerical approach for studying a cantilever bar having a transverse crack. The crack is modeled by an elastic longitudinal spring with a stiffness K according to Castiglione’s theorem.Design/methodology/approachThe bar is excited by different longitudinal impulse forces. The considered problem based on the differential equation of motion is solved by the method of characteristics (MOC) after splitting the second-order motion equation into two first-order equivalent equations.FindingsIn this study, effects of the crack size and crack’s position on the reflected waves from the crack are investigated. The results indicate that the presence of the crack in the cantilever bar generates additional waves caused by the reflection of the incident wave by the crack.Originality/valueA numerical approach developed in this paper is used for detecting the extent of the damage in cracked bars by the measurement of the difference between the dynamic response of an uncracked bar and a cracked bar. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Structural Integrity Emerald Publishing

Dynamic analysis of a cracked bar by the method of characteristics

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
1757-9864
DOI
10.1108/ijsi-01-2018-0001
Publisher site
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Abstract

The purpose of this paper is to introduce a new numerical approach for studying a cantilever bar having a transverse crack. The crack is modeled by an elastic longitudinal spring with a stiffness K according to Castiglione’s theorem.Design/methodology/approachThe bar is excited by different longitudinal impulse forces. The considered problem based on the differential equation of motion is solved by the method of characteristics (MOC) after splitting the second-order motion equation into two first-order equivalent equations.FindingsIn this study, effects of the crack size and crack’s position on the reflected waves from the crack are investigated. The results indicate that the presence of the crack in the cantilever bar generates additional waves caused by the reflection of the incident wave by the crack.Originality/valueA numerical approach developed in this paper is used for detecting the extent of the damage in cracked bars by the measurement of the difference between the dynamic response of an uncracked bar and a cracked bar.

Journal

International Journal of Structural Integrity – Emerald Publishing

Published: Aug 7, 2019

Keywords: Wave propagation; Crack; Method of characteristics; Impulse forces; Longitudinal spring

References

  • An introduction to the method of characteristics
    Abbott, M.B.
  • Generation of higher harmonics in longitudinal vibration of beams with breathing cracks
    Broda, D.; Pieczonka, L.; Hiwarkar, V.R.; Staszewski, W.J.; Silberschmidt, V.V.
  • Modal analysis of a cracked beam
    Chati, M.; Rand, R.; Mukherjee, S.
  • A consistent cracked bar vibration theory
    Chondros, T.G.; Dimarogonas, A.D.; Yao, J.
  • Longitudinal vibration of a bar with a breathing crack
    Chondros, T.G.; Dimarogonas, A.D.; Yao, B.J.
  • Free and forced longitudinal vibrations of a cantilevered bar with a crack
    Collins, K.R.; Plaut, R.H.; Wauer, J.
  • Calcul graphique des régimes variables dans les canaux
    Craya, A.
  • Lamb waves for the non-destructive inspection of monolithic and sandwich composite beams
    Diamanti, K.; Soutis, C.; Hodgkinson, J.M.
  • Crack identification in beams using wavelet analysis
    Douka, E.; Loutridis, S.; Trochidis, A.
  • Crack as modulator, detector and amplifier in structural health monitoring
    Hiwarkar, V.; Babitsky, V.; Silberschmidt, V.; Hiwarkar, V.R.; Babitsky, V.I.; Silberschmidt, V.V.
  • Analyses of flexural wave propagation through beams with a breathing crack using wavelet spectral finite element method
    Joglekar, D.M.; Mitra, M.
  • Analysis of longitudinal wave propagation in a cracked rod by spectral element method
    Magdalena, P.; Krawczuk, M.
  • Mémoire sur l’intégration graphique des équations aux dérivées partielles
    Massau, J.
  • Damage identification in framed structures using natural frequencies
    Nenad Bicanic, H.-P.C.
  • Soil transients by characteristics method
    Papadakis, C.
  • Simple static and dynamic models for the cracked elastic beam
    Petroski, H.J.
  • Applied numerical methods for engineers and scientists
    Rao, S.S.
  • Identification of crack location and magnitude in a cantilever beam from the vibration modes
    Rizos, R.F.; Aspragathos, N.; Dimarogonas, A.D.
  • Approximate analytical method for damage detection in Beam
    Sayyad, F.B.; Kumar, B.
  • Approximate analytical method for damage detection in free–free beam by measurement of axial vibration
    Sayyad, F.B.; Kumar, B.; Khan, S.A.
  • Sensitivity analysis of crack detection in beam by wavelet technique
    Ser-Tang, Q.; Wang, Q.; Zhang, L.; Ang., K.-K.
  • Guided Lamb waves for identification of damage in composite structures: a review
    Su, Z.; Ye, L.; Lu, Y.