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

TL;DR

This paper introduces three novel Arnoldi-type algorithms designed to improve modal and critical speed analysis in damped rotor dynamics FE models, demonstrating superior accuracy over existing methods.

Contribution

The paper presents three new Arnoldi-type methods for quadratic eigenvalue problems in rotor dynamics, utilizing different Krylov subspaces for enhanced accuracy.

Findings

The proposed methods outperform existing Arnoldi-type methods in accuracy.

Numerical examples with turbofan engine rotors validate the effectiveness of the new methods.

The methods facilitate faster and more precise modal analysis 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.