Substructuring approach to the calculation of higher-order eigensensitivity

Weng, Shun; Zhu, Hongping; Xia, Yong; Zhou, Xiao Qing; Mao, Ling

doi:10.1016/j.compstruc.2012.11.005

Cited by 36 publications

(23 citation statements)

References 28 publications

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“…In some forward substructuring methods [3][4][5][6][7][8][9][10][11][12][13][14], only a few lower modes of a substructure are calculated to assemble the global structure while the residual flexibility matrix is required for the compensation of the higher modes. In consequence, the residual flexibility and its derivative matrices are required for the calculation of the eigensolutions and eigensensitivity [9][10][11][12]. The detailed substructuring method will be described in the next section.…”

Section: Calculation Of Residual Flexibility and Its Derivativementioning

confidence: 99%

“…In general, the substructuring approach can be utilized in the forward and inverse manners, respectively. The forward substructuring approach is frequently found in the eigenanalysis of a structure [5][6][7][8][9][10][11][12][13][14]. The partitioned substructures are analyzed independently to obtain their designated solutions, such as the substructural eigensolutions and eigensensitivity.…”

Section: Introductionmentioning

confidence: 99%

“…This paper addresses some frequently encountered difficulties associated with the analysis of the free-free substructures when the authors studied the substructuring methods in the previous research [5,[9][10][11][12][13][14][15][16]. A new full-rank stiffness matrix is proposed, which leads to a well-conditioned eigenequation.…”

Section: Introductionmentioning

confidence: 99%

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Construction of Stiffness and Flexibility for Substructure-Based Model Updating

Weng

Zhu

Xia

et al. 2013

Mathematical Problems in Engineering

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In substructuring methods, the substructures are independently analyzed under free-free conditions. For a free-free substructure, its stiffness matrix is singular and rank deficient due to rigid body motion. The variables associated with the inverse of the stiffness matrix are not easy to be accurately determined in the usual manner. This study expands on the previous research on the substructuring methods by taking a deeper look at the analysis of a free-free substructure. A well-conditioned stiffness matrix is constructed for the analysis of a free-free structure. Some difficulties associated with the analysis of the free-free substructures can be solved in a simple and effective way. The substructural eigensolutions and eigensensitivity are solved from the well-conditioned stiffness matrix, other than the singular stiffness matrix. The proposed well-conditioned eigenequation is accurate and efficient to calculate the substructural eigensolutions and eigensensitivity. The properties addressed in this paper are not limited to be used for the analysis of a free-free substructure in many substructuring methods, and they are promising to be generalized to a range of analysis relevant to a free-free structure.

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Section: Calculation Of Residual Flexibility and Its Derivativementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Construction of Stiffness and Flexibility for Substructure-Based Model Updating

Weng

Zhu

Xia

et al. 2013

Mathematical Problems in Engineering

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“…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].…”

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confidence: 99%

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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“…It has been proved that the substructuring methods are efficient in dealing with large-scale structures, as it takes the local area as an independent structure [4][5][6][7][8][9]. First, the global structure is divided rationally into several smaller substructures to make it much easier and faster to analyze the small substructures independently.…”

Section: Introductionmentioning

confidence: 99%

Substructuring Method in Structural Health Monitoring

Weng¹,

Zhu²,

Xia³

et al. 2017

Structural Health Monitoring - Measurement Methods and Practical Applications

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In sensitivity-based finite element model updating, the eigensolutions and eigensensitivities are calculated repeatedly, which is a time-consuming process for large-scale structures. In this chapter, a forward substructuring method and an inverse substructuring method are proposed to fulfill the model updating of large-scale structures. In the forward substructuring method, the analytical FE model of the global structure is divided into several independent substructures. The eigensolutions of each independent substructure are used to recover the eigensolutions and eigensensitivities of the global structure. Consequently, only some specific substructures are reanalyzed in model updating and assembled with other untouched substructures to recover the eigensolutions and eigensensitivities of the global structure. In the inverse substructuring method, the experimental modal data of the global structure are disassembled into substructural flexibility. Afterwards, each substructure is treated as an independent structure to reproduce its flexibility through a model-updating process. Employing the substructuring method, the model updating of a substructure can be conducted by measuring the local area of the concerned substructure solely. Finally, application of the proposed methods to a laboratory tested frame structure reveals that the forward and inverse substructuring methods are effective in model updating and damage identification.

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Substructuring approach to the calculation of higher-order eigensensitivity

Cited by 36 publications

References 28 publications

Construction of Stiffness and Flexibility for Substructure-Based Model Updating

Construction of Stiffness and Flexibility for Substructure-Based Model Updating

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

Substructuring Method in Structural Health Monitoring

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