The Dynamic Stiffness Method for Linear Rotor-Bearing Systems

Abstract

The behavior of linear rotor-bearing systems is investigated by using the exact approach of the dynamic stiffness method, which entails the use of continuous rather than lumped models. In particular, the theoretical formulation for rotor systems with anisotropic bearings is developed by utilizing the complex representation of all the involved variables. The proposed formulation eventually leads to the 8 × 8 complex dynamic stiffness matrix of the rotating Timoshenko beam; this matrix proves to be related, by a simple rule, to the 4 × 4 dynamic stiffness matrix, which describes rotor systems with isotropic bearings. The method is first applied to the critical speeds evaluation of a simple rotor system with rigid supports; for this case, the exact results of the dynamic stiffness approach are compared to the usual convergence procedure of the finite element method. Successively, the steady-state unbalance response of two rotor systems with anisotropic supports is analyzed; for these examples, the dynamic stiffness results compare favorably with the results of the finite element and the transfer matrix analysis performed by other authors.