Nonlinear analysis of the orbital motions of immersed rotors using a spectral/Galerkin approach

Abstract

We recently 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 δ= H/ R≈0.1––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. 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 nonisotropic supports ( K st Y / K st X =0.4, where K st X and K st Y stand for the structural stiffnesses), which exhibit interesting dynamics, 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. With the proposed symbolic-numerical approach one can obtain accurate nonlinear dynamical formulations enabling the study, understanding and prediction of nonlinear orbital rotor dynamics.