Super-Element Differential-Quadrature Discrete-Time Transfer Matrix Method for Efficient Transient Analysis of Rotor Systems

Abstract

Efficient transient analysis is critical in rotor dynamics. This study proposes the super-element (SE) differential-quadrature discrete-time transfer matrix method (DQ-DT-TMM), a novel approach that eliminates the requirement for initial component accelerations and effectively handles beam and solid finite element (FE) models with high-dimensional degrees of freedom (DOFs) in rotor systems. The primary methodologies of this approach include: (1) For the beam substructure FE dynamic equation, the Craig–Bampton method is employed for the order reduction of internal coordinates, followed by the differential-quadrature method for temporal discretization. Using SE technology, the internal accelerations are condensed into the boundary accelerations, and the transfer equation and matrix for beam SEs are derived. (2) For the solid substructure FE dynamic equation formulated in the rotating reference frame, in addition to applying the procedures used for beam substructures, rigid multipoint constraints are introduced to condense the boundary coordinates for hybrid modeling with lumped parameter components. The transfer equation is subsequently formulated in the inertial reference frame, enabling the derivation of the transfer matrix for solid SEs. Comparative analysis with full-order FE models in commercial software demonstrates the advantages of the SE DQ-DT-TMM for linear rotor systems: (i) Accurately captures system dynamics using only a few primary modes. (ii) Achieves a 99.68% reduction in computational time for a beam model with 1120 elements and a 99.98% reduction for a solid model with 75 361 elements. (iii) Effectively recovers dynamic responses at any system node using recovery techniques. This research develops a computationally efficient framework for the transient analysis of large-scale rotor systems, effectively addressing the challenges associated with high-dimensional DOF models in conventional DT-TMMs.