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Analytical modelling and vibration analysis of cracked rectangular plates with different loading and boundary conditions

Israr, Asif and Cartmell, Matthew P. and Manoach, Emil and Trendafilova, Irina and Ostachowicz, Wieslaw and Krawczuk, Marek and Zak, Arkadiusz (2009) Analytical modelling and vibration analysis of cracked rectangular plates with different loading and boundary conditions. Journal of Applied Mechanics, 76 (1). pp. 11005-11013. ISSN 0021-8936

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Abstract

This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a programme of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminium, and containing a crack in the form of a continuous line with its centre located at the centre of the plate, and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkin's method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Berger's method. An approximate solution technique, the method of multiple scales, is applied to solve the nonlinear equation of the cracked plate. Results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.