Model Order Reduction of a Sliding Beam using a Global Basis: Formulation and Evaluation

Jul 16, 2026

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Model order reduction reduces mechanical-system dimension by using modal coordinates that preserve key dynamics, but sliding beams—common in telescopic structures—exhibit continuously changing effective lengths and boundary conditions. Fixed modal coordinates lose validity, while updating bases makes modal coordinates change meaning. The work builds a single global reduction basis from modal-matrix snapshots, compresses it via proper orthogonal decomposition, and applies it in a constraint multibody formulation with algebraically enforced continuous slider motion. Validation against absolute nodal coordinates shows ~90% computation savings with RMSE displacement error below 2%.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages29

Reading Time1 h 13 min

Abstract

Method Overview

Validation and Error Analysis

Applications in Telescopic Structures

Introduction and Motivation

arXiv :2607 . 1 1794v 1 [ cs .CE] 13 Jul 2026 Model Order Reduction of a Sliding Beam using a Global Basis: Formulation and Evaluation Sebastian Weyrer 1,2 , Johannes Gerstmayr2 , Aki Mikkola 1 , Grzegorz Orzechowski 1* 1 Department of Mechanical Engineering, Lappeenranta-Lahti University of Technology, Lappeenranta and Lahti, Finland. 2 Department of Mechatronics, University of Innsbruck, Technikerstraße 13, Innsbruck, 6020, Tyrol, Austria. *Corresponding author(s). E-mail(s): [grzegorz.orzechowski@lut.fi](grzegorz.orzechowski@lut.fi) ; Contributing authors: [sebastian.weyrer@uibk.ac.at](sebastian.weyrer@uibk.ac.at) ; [johannes.gerstmayr@uibk.ac.at](johannes.gerstmayr@uibk.ac.at) ; [aki.mikkola@lut.fi](aki.mikkola@lut.fi) ; 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% . Keywords: Sliding Beam, Parametric Model Order Reduction, Global Reduction, Proper Orthogonal Decomposition, Real-Time Simulation 1 1 Introduction Telescopic structures are a fundamental component of heavy machinery. They are used in cranes, aerial work platforms, telehandlers, and forestry machines, where adjustable reach is an operational requirement. Telescopic booms enable machines to vary their working radius from a compact transport configuration to full extension. At the sametime, they present a demanding challenge. As a telescoping boom expands, its structure becomes increasingly flexible, and managing dynamic loads requires a thorough understanding of structural behaviors throughout the range of motion. The sliding beams inherent in telescopic booms are defining mechanical features because their effective lengths and Boundary Conditions (BCs) change continuously. These parameter-dependent topology changes make modeling and simulation particularly challenging, an issue addressed, for example, by Steinbrecher et al. [1] and Humeret al. [2] . However, the computational cost of high-fidelity discretizations remains an obstacle, especially when simulations must be performed repeatedly in the context of design optimization or real-time applications. Model Order Reduction (MOR) offers a well-established remedy for large-scale discretized flexible systems. The foundational works of Hurty [3] and Craig and Bampton [4] demonstrate that a structure’s dynamic behavior can be captured accurately using a small set of modal coordinates. However, classical reduction techniques assume fixed topologies: the mode shapes are computed once and remain valid throughout the simulation. This assumption breaks down for sliding beams, where effective lengths, BCs, and mode shapes change continuously as beams extend or retract. A straightforward application of classical reduction would require recomputing and replac

FAQs

为什么滑动梁的经典模态降阶方法难以直接适用？

滑动梁在伸缩过程中有效长度与边界条件持续变化，导致模态形状不再保持固定。经典方法假设拓扑不变，因此会失去精度。

本文如何构建用于滑动梁的全局降阶基？

通过从模态矩阵快照生成全局降阶基，再采用适当正交分解（POD）对快照进行压缩，形成在参数范围内适用的单一基底。

该方法在计算效率和精度上达到什么效果？

与绝对结点坐标（ANCO）滑动梁表述对比，计算时间约降低90%，且由全局降阶引入的位移均方根误差保持在2%以内。

Jul 16, 2026

Upload by Ophelia