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This paper presents the vibratory behavior of a spinning composite shaft with curvilinear fibers on rigid bearings in the case of free vibrations. A p-version of finite element is used to define the model. A theoretical study allows the establishment of the kinetic energy and the strain energy of the shaft, necessary to the result of the equations of motion. In this model the transverse shear deformation, rotary inertia and gyroscopic effects have been incorporated. A hierarchical beam finitedoi:10.1590/1679-78253326 fatcat:sivrxtvkyzc3fndafyxrho3ox4