Global modes for the reduction of flexible multibody systems

Cammarata, Alessandro

doi:10.1007/s11044-021-09790-0

Cited by 8 publications

(11 citation statements)

References 53 publications

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“…For instance, in the left panel of Fig. 2, the backbone curve is well converged at O(3) expansion for amplitude ρ ≤ 0.2, at O (7) for amplitude ρ ≤ 0.3 and at O (13) for amplitude ρ ≤ 0.35.…”

Section: Autonomous Dynamicsmentioning

confidence: 88%

“…We note that this regularity assumption is already satisfied when M is non-singular and the constraints g are not redundant. The eigenvectors corresponding to the infinite eigenvalues are called constraint modes [7,32]. Further details about the spectrum of the linear part of the DAE system (1) are given in Appendix D.…”

Section: System Setupmentioning

confidence: 99%

“…In systems comprising many bodies, this may result in an excessive number of variables in the reduced-order model (ROM). To overcome this issue, projection-based reduction methods based on global flexible modes have been proposed recently [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Model reduction for constrained mechanical systems via spectral submanifolds

Jain

Haller

2023

Nonlinear Dyn

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Dynamical systems are often subject to algebraic constraints in conjunction with their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic compatibility between the motion of different bodies. A full-scale numerical simulation of such constrained problems is challenging, making reduced-order models (ROMs) of paramount importance. In this work, we show how to use spectral submanifolds (SSMs) to construct rigorous ROMs for mechanical systems with configuration constraints. These SSM-based ROMs enable the direct extraction of backbone curves and forced response curves and facilitate efficient bifurcation analysis. We demonstrate the effectiveness of this SSM-based reduction procedure on several examples of varying complexity, including nonlinear finite-element models of multibody systems. We also provide an open-source implementation of the proposed method that also contains all details of our numerical examples.

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Section: Autonomous Dynamicsmentioning

confidence: 88%

Section: System Setupmentioning

confidence: 99%

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Model reduction for constrained mechanical systems via spectral submanifolds

Jain

Haller

2023

Nonlinear Dyn

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show abstract

Section: System Setupmentioning

confidence: 99%

Model reduction for constrained mechanical systems via spectral submanifolds

Li¹,

Jain²,

Haller³

2022

Preprint

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Dynamical systems are often subject to algebraic constraints in conjunction to their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic compatibility between the motion of different bodies. A full-scale numerical simulation of such constrained problems is challenging, making reduced-order models (ROMs) of paramount importance. In this work, we show how to use spectral submanifolds (SSMs) to construct rigorous ROMs for mechanical systems with configuration constraints. These SSM-based ROMs enable the direct extraction of backbone curves and forced response curves, and facilitate efficient bifurcation analysis. We demonstrate the effectiveness of this SSM-based reduction procedure on several examples of varying complexity, including nonlinear finite-element models of multi-body systems. We also provide an open-source implementation of the proposed method that also contains all details of our numerical examples.Keywords Invariant manifolds ¨Reduced-order models ¨Spectral submanifolds ¨Configuration constraints ¨Forced response curves 1 Introduction Constrained mechanical systems arise in a number of engineering applications. In multibody dynamics, for instance, different components of a multibody system are connected by joints that impose kinematic configu-

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“…One strategy used by researchers is the use of reduced-order models (ROMs). For plane systems, an approach using classical Lagrange equations is presented in [27]. The method can be extended to three-dimensional systems.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

2022

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This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

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Global modes for the reduction of flexible multibody systems

Cited by 8 publications

References 53 publications

Model reduction for constrained mechanical systems via spectral submanifolds

Model reduction for constrained mechanical systems via spectral submanifolds

Model reduction for constrained mechanical systems via spectral submanifolds

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

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