This paper is concerned with the dynamic behavior of the rotating composite shaft on rigid bearings. A p-version, hierarchical finite element is employed 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, as well as the coupling effect due to the lamination of composite layers have been incorporated. A hierarchical beam finite element with six degrees of freedom per node is developed and used to find the natural frequencies of a rotating composite shaft. A program is elaborate for the calculation of the eigenfrequencies and critical speeds of a rotating composite shaft. To verify the present model, the critical speeds of composite shaft systems are compared with those available in the literature. The efficiency and accuracy of the methods employed are discussed.
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