The main goal of this paper is to use a very new High Order Shear Deformation Theory (HSDT) approach in order to model the vibrations of a homogenous composite bar with elastic symmetry and presenting a rectangular section. The method which is proposed consists in assuming a certain form of elastic third order displacements field. The originality consists that this field is described as follows: it respects the Saint-Venant conditions, some of the Cauchy conditions and, for the first time, the Gay conditions for bars.
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