Three New Arnoldi-Type Methods for the Quadratic Eigenvalue Problem in Rotor Dynamics

Abstract: Three new Arnoldi-type methods are presented to accelerate the modal analysis and critical speed analysis of the damped rotor dynamics finite element (FE) model. They are the linearized quadratic eigenvalue problem (QEP) Arnoldi method, the QEP Arnoldi method, and the truncated generalized standard eigenvalue problem (SEP) Arnoldi method. And, they correspond to three reduction subspaces, including the linearized QEP Krylov subspace, the QEP Krylov subspace, and the truncated generalized SEP Krylov subspace, where the first subspace is also used in the existing Arnoldi-type methods. The numerical examples constructed by a turbofan engine low-pressure (LP) rotor demonstrate that our proposed three Arnoldi-type methods are more accurate than the existing Arnoldi-type methods.