In this paper, Carrera's unified formulation (CUF) is used to perform free-vibrational analyses of rotating structures. The CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials of N-order, in which N is a free parameter. Linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of rotors. The finite element method is used to derive the governing equations in weak form. These equations are written in terms of few fundamental nuclei, whose forms do not depend on the approximation used (N). In order to assess the new theory, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. Among the considered test cases, a rotor with deformable disk is considered and the results show the convenience of using refined models since that are able to include the in plane deformability of disks.

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