Nonlinear flexural free vibrations of thin circular rings: An explicit approach


M. Rougui1*, F. Moussaoui2, M. Masrar3, R. Benamar4

1  LAMNAS,UFR de Mécanique, B.P 6261 Al Adarissa, FST de Fès, Maroc

2 Laboratoire de Mécanique et Calcul Scientifique. FS T, BP 509, Boutalamine, Errachidia, Maroc

3 LAMNAS, UFR de Mécanique, B.P 6261 Al Adarissa, FST de Fès, Maroc

4  Modélisation Laboratoire d4Etudes et de Recherches en Simulation Instrumentation et Mesures, Ecole Mohammadia d'Ingénieurs, Avenue Ibn Sina B.P 765 Agdal, Rabat, Maroc

* Corresponding author. E-mail:
Received: 04 April 2006; revised version accepted: 24 July 2007



     An investigation of the non-linear flexural vibrations of thin isotropic circular rings is presented. Free vibrations at large amplitudes are analysed by using an explicit approach developed previously for beams and plates. This approach, which combines Lagrange's formulation with the Harmonic balance method, is extended here to structures with curvatures, i.e. circular rings. The Donnell's non-linear thin shell theory has been employed and the transverse displacement expression has been chosen following some assumptions. A non-linearity of the softening type has been obtained, and the results have been compared with the available theoretical data, showing a good agreement. It can be concluded from this study that the present approach, which is much simpler and more straightforward than most of those classically used in the literature, can lead to engineering formulae which are very close to those obtained by other sophisticated methods, such as the FEM and the perturbation methods. These formulae may be easily implemented in the fatigue models and the design procedures.


Keywords: Nonlinear; Vibration; Circular ring; Flexural; Explicit method.

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