Model Order Reduction of a Sliding Beam using a Global Basis: Formulation and Evaluation
2026-07-13 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors developed a way to simplify the simulation of sliding beams, like those in telescopic structures, by creating a single global basis that captures the system's behavior over time. Instead of changing the modal coordinates during the simulation, which causes confusion, they combined multiple snapshots of the system's modes into a compressed form using proper orthogonal decomposition. Their method works with a special multibody framework that allows the sliding part to move smoothly and was tested against an established modeling approach. They found that their global reduction technique makes simulations run about 90% faster while keeping the errors very low, under 2%.
model order reductionmodal coordinatessliding beamtelescopic structureproper orthogonal decompositionmultibody dynamicsalgebraic constraintsmodal basisroot-mean-square errorsimulation
Authors
Sebastian Weyrer, Johannes Gerstmayr, Aki Mikkola, Grzegorz Orzechowski
Abstract
Model order reduction decreases the dimension of a mechanical system by introducing modal coordinates that retain important dynamic characteristics. Sliding beams, as found in telescopic structures, pose a fundamental challenge. Fixed modal coordinates fail to capture evolving system properties, and updating the modal basis during simulation causes modal coordinates to change meaning. The present work addresses this challenge by constructing a global reduction basis for a sliding beam. The global basis is constructed from snapshots in the form of modal matrices and compressed using proper orthogonal decomposition. Reduction is applied within a constraint multibody formalism with algebraically enforced constraints that permit continuous slider movement. The method is validated against an absolute nodal coordinate formulation of a sliding beam with a sliding joint. Different combinations of snapshot quantity and eigenmodes per snapshot are investigated and an error map is shown. A challenging test case involving a highly flexible beam subjected to time-dependent loading and slider movement demonstrates that the global reduction basis reduces computation time by approximately 90% while keeping the root-mean-square displacement error, introduced by the global reduction, below 2%.