Time Integration of Dual Craig-Bampton Reduced Systems

Gruber, Fabian; Gille, Max; Rixen, Daniel J.

doi:10.7712/120117.5481.17213

Cited by 3 publications

(2 citation statements)

References 15 publications

(40 reference statements)

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“…The original Lagrange multipliers may cause nonphysical eigensolutions in the reduced models. It can be alleviated with a subsequent step proposed by Gruber et al 8 The other free interface CMS method known as flexibility‐based CMS (F‐CMS) method was also proposed by Park and Park 9 . Unlike the dual CB method, the localized Lagrange multipliers were utilized in the F‐CMS method.…”

Section: Introductionmentioning

confidence: 99%

An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

Chung

Kim²,

Chae

et al. 2021

Numerical Meth Engineering

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An Iterative Flexibility‐based Component Mode Synthesis (IF‐CMS) is presented for the model reduction of partitioned structural dynamic systems via localized Lagrange multipliers. A distinct IF‐CMS feature is the inclusion of hierarchical residual flexibility at each iteration, resulting in considerably improved accuracy compared with the classical Craig–Bampton (CB) CMS method. The present IF‐CMS method does not increase the number of substructural modes during the hierarchical iteration process. In particular, to alleviate ill‐conditioning during the iteration steps, the proposed IF‐CMS method adopts the so‐called (qd, α, ub)‐formulation by condensing Lagrange multipliers from the original F‐CMS method. The performance of the proposed method is evaluated through numerical examples, which illustrates improved accuracy over existing CMS methods.

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Section: Introductionmentioning

confidence: 99%

An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

Chung

Kim²,

Chae

et al. 2021

Numerical Meth Engineering

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“…This renders a straightforward time integration of the DCBM reduced system impossible. In [10], the unstable behavior when time-integrating DCBM reduced systems without further modifications is illustrated and an approach to overcome this instability is suggested: a modal analysis of the reduced system is performed as a subsequent step to the dual Craig-Bampton reduction. Only modes corresponding to positive eigenvalues are retained for transient analysis.…”

Section: Introductionmentioning

confidence: 99%

Accurate Computation of Frequency Response Functions of Dual Craig-Bampton Reduced Systems

Gruber¹,

Stahl²,

Rixen³

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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The dual Craig-Bampton method (DCBM) employs modes with free interfaces to build the reduction bases of the substructures, but assembles the substructures using interface forces, which is called dual assembly. The DCBM preserves the sparsity of the final reduced mass and stiffness matrices similar to the classical Craig-Bampton reduced matrices, which makes the reduced matrices simpler and less populated than the reduced matrices of other free interface methods. However, the DCBM is not a Rayleigh-Ritz transformation only on the displacement degrees of freedom, but reduces the dually assembled system. Thereby, interface kinematic conditions are transformed, allowing incompatibilities between the substructures unlike other substructuring techniques. This interface kinematic transformation enforces only a weak displacement compatibility between the substructures. As a consequence, the reduced-order model always has as many negative eigenvalues as Lagrange multipliers used for the dual assembly. When applying a DCBM reduction, the reduced system is no longer positive (semi)definite. This means that the reduced system is unstable. Although rendering direct time integration impossible, this does not affect the computation of frequency response functions (FRFs), which is demonstrated in this paper. The feasibility of a reliable and accurate FRF computation of DCBM reduced systems is investigated in detail. Hereby, DCBM reduced system means that a reduced system after a DCBM reduction is used without any modifications. It is demonstrated that the unstable behavior of the DCBM reduced system does not negatively influence the computation of the FRFs. Following this, methods for the further reduction are evaluated: modal reduction and interface reduction are applied to the DCBM reduced system. Moreover, the reduced system is enhanced by incorporating modal truncation vectors. This guarantees static correctness and enables a very accurate approximation of antiresonances. This is illustrated by three different examples. Thereby, the resulting FRFs of the DCBM reduced systems are compared to the FRFs of the unreduced systems.

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Dual Craig-Bampton component mode synthesis method for model order reduction of nonclassically damped linear systems

Gruber

Rixen

2018

Mechanical Systems and Signal Processing

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Time Integration of Dual Craig-Bampton Reduced Systems

Cited by 3 publications

References 15 publications

An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

An iterative scheme of flexibility‐based component mode synthesis with higher‐order residual modal compensation

Accurate Computation of Frequency Response Functions of Dual Craig-Bampton Reduced Systems

Dual Craig-Bampton component mode synthesis method for model order reduction of nonclassically damped linear systems

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