On-the-fly reduced-order modeling for vibration analysis of three-dimensional finite element-based rotating systems

This work presents a model-order reduction framework for three-dimensional finite element-based rotating systems parameterized by rotational speed. To address potential vibration problems in linearized rotor dynamics, both co-rotating and fixed-reference frames are considered to establish governing equations in the time, frequency, and modal domains. The proposed approach represents solutions to these equations as a low-rank approximation. Based on this approximation, a nonlinear equation is formulated and a unified algorithmic framework is developed with specific derivations tailored for each analysis domain. Basis vectors spanning the low-dimensional subspace are progressively enriched on-the-fly without solving the full-order model. Solutions at evaluation points are obtained using the reduced-order model based on Galerkin projection. The performance of the proposed approach is examined through numerical examples, demonstrating its ability to provide accurate solutions across various analysis domains. Additionally, by replacing the direct computation of full-order models at evaluation points with the acquisition of basis vectors and solving reduced-order models, computational efficiency is significantly enhanced.