An iterative substructuring approach to the calculation of eigensolution and eigensensitivity

Weng, Shun; Xia, Yong; Xu, You Lin; Zhu, Hongping

doi:10.1016/j.jsv.2011.02.001

Cited by 52 publications

(47 citation statements)

References 21 publications

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“…Consequently, the precision of all the interested modes can be improved simultaneously. This is quite different from the existing exact modal synthesis methods [11,20,23,34]. As it basically does not resort to any approximation, the proposed method could achieve accurate results with higher computational efficiency.…”

mentioning

confidence: 70%

“…Recently, Weng et al improved the Kron's method for practical engineering applications. Instead of directly following the definition, their methods calculate the receptance matrix with either the first-order approximation [33] or an iterative procedure [34]. This improvement reduces the computational cost and in the meantime provides the feasibility for further eigensensitivity analyses [35].…”

mentioning

confidence: 99%

“…This improvement reduces the computational cost and in the meantime provides the feasibility for further eigensensitivity analyses [35]. Moreover, compared with the approximation-based methods, the iterative methods can be more effective when accurate results are required [34]. Nevertheless, in the existing iterative procedure, the precision of modes has to be improved one by one as a result of the eigenvalue-dependent reduced stiffness matrix, which may include extra computational cost [36].…”

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confidence: 99%

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A simultaneous iterative procedure for the Kron's component modal synthesis approach

Cui

Guan

Zheng

2015

Int. J. Numer. Meth. Engng

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A simultaneous iterative procedure for the Kron's component modal synthesis method is developed in this paper for fast calculating the modal parameters of a large-scale and/or complicated structure. To simultaneously improve the precision of all the concerned modal parameters, the modal transformation matrix is chosen as the iterative term. For a faster convergence rate, the reduced system matrices are consistent with the modal transformation matrix. With a mathematically proved consistency and reasonably justified convergence, the proposed method can provide highly accurate results after a few iterations. The implementation details are presented for reference together with some computational considerations. Compared with other methods for obtaining modal parameters, the proposed method has such merits as high computational efficiency and still in a substructuring scheme. Two numerical examples are provided to illustrate and validate the proposed method. SIMULTANEOUS ITERATIVE COMPONENT MODAL SYNTHESIS METHOD 991 the dual [13,18] or field-consistent [19] assembling; and so on. Among these approaches, the Kron's CMS method [13] has some distinct advantages in dealing with large-scale structures. Firstly, it is a free-interface method, and thus, the size of the reduced model is not related to the number of interface degrees of freedom (DOFs). Besides, it can be combined with the test data [5,6,24,25]. Secondly, it assembles the components in dual form [5,18] and thus can deal with cases when two or more components are assembled under complicated interface conditions. The Kron's CMS method was firstly developed by Kron in his book Diakoptics [26] for electrical problems and then modified for structural problems via the receptance matrix by Simpson et al. [27]. Some early works improved the method from the perspectives of theoretical [28,29] and numerical [30][31][32] considerations. Recently, Weng et al. improved the Kron's method for practical engineering applications. Instead of directly following the definition, their methods calculate the receptance matrix with either the first-order approximation [33] or an iterative procedure [34]. This improvement reduces the computational cost and in the meantime provides the feasibility for further eigensensitivity analyses [35]. Moreover, compared with the approximation-based methods, the iterative methods can be more effective when accurate results are required [34]. Nevertheless, in the existing iterative procedure, the precision of modes has to be improved one by one as a result of the eigenvalue-dependent reduced stiffness matrix, which may include extra computational cost [36]. Thus, some further improvement in the iterative procedure may still be needed for enhancing the computational efficiency.This paper suggests a simultaneously iterative procedure for the Kron's CMS method. With this method, the modal transformation matrix, instead of eigenvalues, is chosen to be improved iteratively. Consequently, the precision of all the interested modes can be improved simult...

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A simultaneous iterative procedure for the Kron's component modal synthesis approach

Cui

Guan

Zheng

2015

Int. J. Numer. Meth. Engng

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“…The analytical FE model of the structure [ Fig. 13(b)] includes 8,738 three-dimensional elements, 3,671 nodes (each of which has six DOFs), and 21,690 DOFs [6].…”

Section: Case Study 2: the Guangzhou New Television Towermentioning

confidence: 99%

“…The substructuring approach is potentially efficient in the model updating of large-scale structures [4][5][6][7] and related applications [8][9][10]. In these studies, the global structure is divided into smaller and more manageable substructures.…”

Section: Introductionmentioning

confidence: 99%

Inverse substructure method for model updating of structures

Weng¹,

Xia²,

Zhou³

et al. 2012

Journal of Sound and Vibration

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Traditional model updating of large-scale structures is usually time-consuming because the global structural model needs to be repeatedly re-analyzed as a whole to match global measurements. This paper proposes a new substructural model updating method. The modal data measured on the global structure are disassembled to obtain the independent substructural dynamic flexibility matrices under force and displacement compatibility conditions. The method is extended to the case when the measurement is carried out at partial degrees-of-freedom of the structure. The extracted substructural flexibility matrices are then used as references for updating the corresponding substructural models. An orthogonal projector is employed on both the extracted substructural measurements and the substructural models to remove the rigid body modes of the free-free substructures. Compared with the traditional model updating at the global structure level, only the sub-models at the substructural level are re-analyzed in the proposed substructure-based model updating process, resulting in a rapid convergence of optimization.Moreover, only measurement on the local area corresponding to the concerned substructures is required, and those on other components can be avoided. The effectiveness and efficiency of the proposed substructuring method are verified through applications to a laboratory-tested frame structure and a large-scale 600 m tall Guangzhou New TV Tower. The present technique is referred to as the inverse substructuring model updating method as the measured global modal data are disassembled into the substructure level and then the updating is conducted on the substructures only. This differs from the substructuring model updating method previously This is the Pre-Published Version. 2 proposed by the authors, in which the model updating is still conducted in the global level and the numerical global modal data are assembled from those of substructures. That can be referred to as the forward substructuring model updating method.

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An eigenvector‐based iterative procedure for the free‐interface component modal synthesis method

Cui

Wang

Xing

et al. 2018

Numerical Meth Engineering

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A novel eigenvector-based iteration procedure is developed for the free-interface component modal synthesis (CMS) method. To derive the iteration formula, Kron's substructuring is employed to distribute the computations of subspace iteration, and the free-interface component modes are chosen as the initial guess. Then, the modal transformation matrix of the first-order approximated Kron's CMS method is proved to be the free-interface component modes with one step of Kron's inverse iteration. The proposed CMS method has the advantages of both free-interface CMS approximation and subspace iteration: on one hand, the CMS approximation provides a high-quality initial guess and distributes the computational cost of the subspace iteration; on the other hand, the subspace iteration provides a more efficient way for truncation compensation and is compatible with using deflation, shifting, and restarting for further enhancements on the efficiency. Numerical examples show that the efficiency of the proposed method is higher than that of the conventional simultaneous iterative Kron's CMS method, especially for obtaining a large number of high-precision modes. Moreover, the proposed method is as efficient as the global Lanczos method for first-time analysis without parallelization while retaining the advantages of CMS methods for reanalysis tasks, parallelization, etc. KEYWORDScomponent modal synthesis, iterative, subspace iteration, substructure Int J Numer Methods Eng. 2018;116:723-740. wileyonlinelibrary.com/journal/nme

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An iterative substructuring approach to the calculation of eigensolution and eigensensitivity

Cited by 52 publications

References 21 publications

A simultaneous iterative procedure for the Kron's component modal synthesis approach

A simultaneous iterative procedure for the Kron's component modal synthesis approach

Inverse substructure method for model updating of structures

An eigenvector‐based iterative procedure for the free‐interface component modal synthesis method

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