Analysis of the Nonlinear Orbital Motions of Immersed Rotors Using a Spectral/Galerkin Approach

Abstract

Recently, we developed a symbolic-numerical formulation for the nonlinear planar motion of rotors under fluid confinement, based on a spectral/Galerkin approach, for gap geometries of about [equação] where H is the average annular gap and R is the rotor radius. Results showed a quite good agreement between the class of approximate models generated, the corresponding analytical exact planar model and experiments. Note that this methodology can be almost entirely automated on a symbolic computing environment. In the present paper this symbolic-numerical spectral/Galerkin procedure is extended in order to deal with nonlinear orbital motions - X (t) and Y (t) taking place in orthogonal directions. Numerical simulations performed over a centered rotor configuration maintained by non-isotropic supports [equação], which exhibit rich rotordynatnics, show a quite good agreement between this type of approximate models and the corresponding analytical exact (but quite involved) model developed in the past by the authors.