A Note on Critical-Speed Solutions for Finite-Element-Based Rotor Models

An ordering scheme is introduced for the deflection variables in finite-element-based rotordynamics models which permits a direct numerical solution approach via symmetric matrix procedures for rotor critical speeds, providing the system stiffness matrix is symmetric. Previously published reports on finite-element formulations employ general Q-R algorithms operating on state-variable forms of the governing equations to obtain rotor natural frequencies at a specified running speed, with critical speeds determined from many such calculations.