On approximate anatytical solutions for vibrations in cracked plates

A. Israr, M.P. Cartmell, M. Krawczuk, W.M. Ostachowicz, E. Manoach, I. Trendafilova, E.V. Shishkina, M. Palacz

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Recent NATO funded research on methods for detection and interpretation methodologies for damage detection in aircraft panel structures has motivated work on low-order nonlinear analytical modelling of vibrations in cracked isotropic plates, typically in the form of aluminium aircraft panels. The work applies fundamental aspects of fracture mechanics to define an elliptical crack, and the local stress field and loading conditions, arbitrarily located at some point in the plate, and then derives an analytical expression for this that can be incorporated into the PDE for an edge loaded plate with various possible boundary conditions. The plate PDE is converted into a nonlinear Duffing-type ODE in the time domain by means of a Galerkin procedure and then an arbitrarily small perturbation parameter is introduced into the equation in order to apply an appropriate solution method, in this case the method of multiple scales. This is used to solve the equation for the vibration in the cracked plate for the chosen boundary conditions, which, in turn, leads to an approximate analytical solution. The solution is discussed in terms of the perturbation approximations that have been applied and highlights the phenomenology inherent within the problem via the specific structures of the analytical solution.
LanguageEnglish
Pages315-322
Number of pages8
JournalApplied Mechanics and Materials
Volume5-6
DOIs
Publication statusPublished - 31 Oct 2006

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Aircraft
Boundary conditions
Damage detection
Fracture mechanics
Cracks
Aluminum

Keywords

  • analytical modeling
  • crack
  • pertubation method of multiple scales
  • plate vibrations
  • resonance conditions

Cite this

Israr, A., Cartmell, M. P., Krawczuk, M., Ostachowicz, W. M., Manoach, E., Trendafilova, I., ... Palacz, M. (2006). On approximate anatytical solutions for vibrations in cracked plates. Applied Mechanics and Materials, 5-6, 315-322. https://doi.org/10.4028/www.scientific.net/AMM.5-6.315
Israr, A. ; Cartmell, M.P. ; Krawczuk, M. ; Ostachowicz, W.M. ; Manoach, E. ; Trendafilova, I. ; Shishkina, E.V. ; Palacz, M. / On approximate anatytical solutions for vibrations in cracked plates. In: Applied Mechanics and Materials. 2006 ; Vol. 5-6. pp. 315-322.
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Israr, A, Cartmell, MP, Krawczuk, M, Ostachowicz, WM, Manoach, E, Trendafilova, I, Shishkina, EV & Palacz, M 2006, 'On approximate anatytical solutions for vibrations in cracked plates' Applied Mechanics and Materials, vol. 5-6, pp. 315-322. https://doi.org/10.4028/www.scientific.net/AMM.5-6.315

On approximate anatytical solutions for vibrations in cracked plates. / Israr, A.; Cartmell, M.P.; Krawczuk, M.; Ostachowicz, W.M.; Manoach, E.; Trendafilova, I.; Shishkina, E.V.; Palacz, M.

In: Applied Mechanics and Materials, Vol. 5-6, 31.10.2006, p. 315-322.

Research output: Contribution to journalArticle

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AU - Israr, A.

AU - Cartmell, M.P.

AU - Krawczuk, M.

AU - Ostachowicz, W.M.

AU - Manoach, E.

AU - Trendafilova, I.

AU - Shishkina, E.V.

AU - Palacz, M.

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