Continuation of nonlinear normal modes using reduced-order models based on generalized characteristic value decomposition

被引:0
|
作者
Stein, Dalton L. [1 ]
Chelidze, David [1 ]
机构
[1] Univ Rhode Isl, Nonlinear Dynam Lab, Kingston, RI 02881 USA
关键词
Characteristic value decomposition; Reduced-order model; Model order reduction; Nonlinear dynamics; Continuation of nonlinear normal modes; PROPER ORTHOGONAL DECOMPOSITION; PART I; REDUCTION; SYSTEMS; IDENTIFICATION; VIBRATION;
D O I
10.1007/s11071-024-10239-0
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
Over the past two decades, data-driven reduced-order modeling (ROM) strategies have gained significant traction in the nonlinear dynamics community. Currently, several challenges in physical interpretation and data availability remain overlooked in current methodologies. This work proposes a novel ROM methodology based on a newly proposed generalized characteristic value decomposition (GCVD) to address these obstacles. The GCVD-ROM approach proposes a new perspective toward data-driven ROMs via characterization of the dynamics before any ROM considerations are made. In doing so, a significant degree of versatility is inherited in the GCVD-ROM strategy, allowing our models to reproduce the full-scale dynamics in different regions of the parameter space at the cost of a single training data set. Our approach utilizes computationally efficient free-decay data sets alongside a windowed-decomposition scheme, allowing us to extract energy-dependent modal structures for use in model-order reduction. This is accomplished using the physically insightful characteristic values provided by the GCVD, which are shown to be directly related to the system poles at a particular response amplitude. This natural metric, paired with a resonance tracking scheme, allows us to address the difficulties associated with physical interpretation and data availability without sacrificing the convenient aspects of linear projection-based model order reduction. A computational framework for the continuation and bifurcation analysis using linear projection-based ROMs is also presented, permitting us to deploy rigorous analysis and bifurcation studies to verify that our ROMs reproduce the intrinsic complexity of full-scale systems. A detailed walk-through of the GCVD-ROM approach is demonstrated on a simple system where important practical considerations and implementation details are discussed using a concrete example. The discretized von K & aacute;rm & aacute;n beam and shallow arch partial differential equations are also used to explore complicated scenarios involving modal coupling across disparate time scales and internal resonances.
引用
收藏
页码:25 / 45
页数:21
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