Damping synthesis using complex substructure modes and a Hermitian system representation

Béliveau, Jean-Guy; Soucy, Y.

doi:10.2514/3.9201

Cited by 21 publications

(6 citation statements)

References 9 publications

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“…(6) and normalize the eigenvectors according to Eq. (10). Note that the complete eigensolution is not necessary.…”

Section: Summary Of the Methodsmentioning

confidence: 96%

“…Beliveau and Soucy [10] developed a modified Craig-Bampton method by replacing the real fixed-interface normal modes with the corresponding complex modes. Craig and Ni [11] generalized the concepts of residual flexibility and residual attachment modes to damped systems and then presented a state-space free-interface component-modesynthesis method that achieves greater model accuracies than those by the previous methods.…”

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confidence: 99%

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Improved Component-Mode Synthesis for Nonclassically Damped Systems

Liu

Zheng

2008

AIAA Journal

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An improved technique of the component-mode synthesis for nonclassically damped systems with the secondorder approximation is proposed in this paper. It is based on free-interface vibration modes and residual attachment modes or residual inertia-relief attachment modes complemented with dynamic effects of the truncated modes. Both nondefective and defective components are considered, and the relationships between them are discussed. A new criterion for the selection of the component vibration modes is developed in the frequency domain. State-level synthesis procedures are naturally employed in the new formulations presented herein. The accuracy and effectiveness of the present synthesis method are demonstrated and are compared with those of the static approach via numerical examples, and also the validity of the modes selection criterion is also proved by these examples. Nomenclature A s , B s = synthesized system matrices C = damping matrix of the component f = external force vector acting on the component I = identity matrix K = stiffness matrix of the component M = mass matrix of the component p = modal coordinate vector T = transformation matrix between independent and dependent modal coordinates x = unknown displacement response vector of the component i = complex eigenvalue of the component = complex spectrum matrix ' i , i = right and left eigenvectors of the component in the state space , = right and left modal matrices in the state space = component mode used for the synthesis d rd , d rd = right and left rigid-body modes in the displacement space Subscripts a = set of residual attachment modes e = set of elastic complex modes ek = set of kept elastic complex modes k = set of kept complex modes r = set of rigid-body modes t = set of truncated complex modes Superscripts = component = component

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“…(6) and normalize the eigenvectors according to Eq. (10). Note that the complete eigensolution is not necessary.…”

Section: Summary Of the Methodsmentioning

confidence: 96%

mentioning

confidence: 99%

Improved Component-Mode Synthesis for Nonclassically Damped Systems

Liu

Zheng

2008

AIAA Journal

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“…• Beliveau and Soucy (1985) proposed another version that modifies the classical Craig-Bampton method to include damping [3]. The real fixed interface normal modes Φ iφ in Eq.…”

Section: Reduction Approaches For Nonclassically Damped Systemsmentioning

confidence: 99%

“…3 Numerical example A simply coupled structure (taken from [3]) with 20 displacement DOFs is used to compare the methods described in Section 2. causes very large errors, especially for the eigenvalue pairs with a small absolute magnitude. Eigenvalues with larger absolute magnitudes are approximated better, but the relative error is still around 10%.…”

Section: Reduction Approaches For Nonclassically Damped Systemsmentioning

confidence: 99%

Overview of Craig‐Bampton Substructuring Approaches for Model Order Reduction of Nonclassically Damped Systems

Gruber

Rixen

2018

Proc Appl Math and Mech

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The classical Craig-Bampton method (1968) does not take any damping effects into account for the model order reduction of damped systems. One procedure to handle nonclassically damped systems is to transform the second-order differential equations into state-space representation. Solving the corresponding eigenvalue problem allows the damped equations to be decoupled, but complex eigenmodes and eigenvalues occur. A comparison between different formulations for nonclassically damped systems is given and demonstrated by an example.

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“…Ref. [1] and [2] adopted complex component modes and extended the Craig-Bampton method to damped systems with symmetric substructure matrices by different patterns. Ref.…”

Section: Introductionmentioning

confidence: 99%