Finite element analysis of dynamic stability of bearingless rotor

Dynamic stability equations of bearingless rotor blades were investigated using a simplified model. The aerodynamic loads of blades were evaluated using two-dimensional airfoil theory. Perturbation equations were obtained by linearization of the perturbation. A normal-mode approach was used to transform the equations expressed by nodal degrees of freedom into equations expressed by modal degrees of freedom, which can reduce the dimension of the equations. The stability results of rotor blades were presented using eigenvalue analysis. The shape function matrix was obtained using spline interpolation, which simplified the analysis and made assembly of the inertial matrix, damping matrix, and stiffness matrix a simple mathematical summation. The results indicate that the method is efficient and greatly simplifies the analysis.