Considering the Higher-Order Effect of Residual Modes in the Craig–Bampton Method

Kim, Jaemin; Boo, Seung-Hwan; Lee, Phill-Seung

doi:10.2514/1.j055666

Cited by 4 publications

(6 citation statements)

References 29 publications

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“…However, the problem is that the angular frequency

ω

is an unknown variable. To handle this issue, iterative model reduction approaches have been considered 19,32‐35 . The i th‐order term

ω^{2 i}

in the new transformation matrix T new is then updated at the ( i − 1)th step.…”

Section: Iterative Formulation By Using the Global Matricesmentioning

confidence: 99%

“…We here compare the IF‐CMS method with the other well‐known iterative CMS methods: Higher‐order CB (HCB) method 30,35 and iterative CB method 31 . Both the HCB and iterative CB methods were directly motivated from the ECB method that is the first CB approach with the residual flexibility 19 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The condition numbers of the reduced matrices become worse through the iteration process. The HCB method and other related methods simply handled this issue with higher precisions such as 32 or 64 digits, 30,35 but the IF‐CMS formulation resolves it by using the preconditioning process within the standard 16 digit precision.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The original ECB method only considers the zeroth order of residual flexibility. Thus, many following works have focused on using higher‐order residual flexibility in the iterative manner 31‐35 . Xing et al 31 improved an accuracy of the CB method with the iterative technique in the similar manner of the iterative improved reduced system (IIRS) method 32 .…”

Section: Introductionmentioning

confidence: 99%

“…The iterative methods may lead enough accurate reduced model by increasing the number of iteration steps, but the major problem is how to control ill‐conditioning that becomes worse than the previous iteration step. Higher precision over 16 digits and/or correction by using reference eigensolutions have been proposed, but this is still significant issue 35 . Go et al recently summarized these approaches well 30 …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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“…However, the problem is that the angular frequency