TY - JOUR

T1 - On approximate analytical solutions for vibrations in cracked plates

AU - Israr, Asif

AU - Cartmell, Matthew P.

AU - Krawczuk, Marek

AU - Ostachowicz, Wieslaw

AU - Manoach, Emil

AU - Trendafilova, I.

AU - Shishkina, E.V.

AU - Palacz, M.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - applied mechanics

KW - vibration

KW - plate vibrations

KW - analytical modelling

KW - resonance conditions

UR - http://www.scientific.net/0-87849-418-9/315/

M3 - Article

VL - 5-6

SP - 315

EP - 322

JO - Applied Mechanics and Materials

JF - Applied Mechanics and Materials

SN - 1660-9336

ER -