Variable kinematic one-dimensional finite elements for the analysis of rotors made of composite materials

This paper deals with the dynamic response of rotors made of anisotropic, laminated composite materials. It is a sequel to the authors' previous work, which was devoted to the rotordynamics of metallic structures. The used variable kinematic one-dimensional models describe any cross-sectional deformation of the rotor and go beyond the plane strain assumptions of classical Euler-Bernoulli and Timoskenko beam theories. Refined theories are obtained by applying the Carrera unified formulation, which is extended here to the rotordynamics of multilayered composites. The displacement variables over the rotor cross section x-z plane are approximated by x, z polynomials of any order N. Thin-walled cylindrical shafts and boxes are analyzed. These structures are made of unidirectional layers, whose fiber orientation can vary with respect to the rotor-axis as well as in the x-z plane. Several analyses have been carried out to determine the vibrational response as a function of the rotating speed. Classical beam theories are obtained as particular cases and results available in the literature, including shell results, are used to assess the presented theory. The proposed refined models are very effective in investigating the dynamic behavior of laminated composite rotors.