Dynamic Analyses of Axisymmetric Rotors Through Three-Dimensional Approaches and High-Fidelity Beam Theories

Abstract

This paper evaluates the differences between two existing ways to derive the governing equations of axisymmetric rotors in an inertial frame of reference. According to the first approach, only a skew-symmetric gyroscopic matrix appears into the equations of motion. In the second approach, besides the gyroscopic term, a convective tensor is obtained from the kinetic energy expression. This contribution is proportional to the square of the rotational speed, and it modifies the elastic energy of the rotor. The weak form of the equations of motion has been solved using high-fidelity one-dimensional finite elements, which have been developed with the Carrera Unified Formulation (CUF). The fundamental nuclei of the gyroscopic and the convective matrices are presented in CUF form, for the first time. To highlight the differences between the two approaches, numerical simulations have been carried out on relatively simple rotor configurations, whose dynamic behaviors were already studied. The current results have been compared with the solutions presented in the literature to verify the correctness of the proposed formulation. For some structures, the results computed with the two approaches differ to a significant extent.