Vol. 3, No. 5, 2008

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A cracked beam finite element for rotating shaft dynamics and stability analysis

Saber El Arem and Habibou Maitournam

Vol. 3 (2008), No. 5, 893–910

In this paper, a method for the construction of a cracked beam finite element is presented. The additional flexibility due to the cracks is identified from three-dimensional finite element calculations taking into account the unilateral contact conditions between the crack lips. Based on this flexibility, which is distributed over the entire length of the element, a cracked beam finite element stiffness matrix is deduced. Considerable gain in computing efforts is reached compared to the nodal representation of the cracked section when dealing with the numerical integration of differential equations in structural dynamics. The stability analysis of a cracked shaft is carried out using the Floquet theory.

breathing crack, beam, unilateral contact, finite element, rotor, Floquet, stability
Received: 23 September 2007
Revised: 9 April 2008
Accepted: 13 April 2008
Published: 1 July 2008
Saber El Arem
Laboratoire de Mécanique des Solides CNRS (UMR 7649)
Ecole Polytechnique
91128 Palaiseau Cedex
Habibou Maitournam
Laboratoire de Mécanique des Solides CNRS (UMR 7649)
Ecole Polytechnique
91128 Palaiseau Cedex