Direct Updating of Damping and Stiffness Matrices

Friswell, Michael I.; Inman, Daniel J.; Pilkey, Deborah F.

doi:10.2514/2.396

Cited by 148 publications

(30 citation statements)

References 13 publications

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“…Equations (19) or (20) su®er from the drawback that the updated matrix may not be symmetric. To remedy such a drawback, Eq.…”

Section: Generalization Of the Theory To Consider The¯rst Few Modesmentioning

confidence: 99%

“…Following the work by Berman and Nagy, 16 Caesar and Peter 18 proposed the direct matrix update (DMU) method for updating free/free and¯xed/free structures satisfying the force equilibrium or total mass conditions, in addition to the orthogonality and eigendynamic constraints. Assuming the mass matrix to be correct, the damping and sti®ness matrices were updated simultaneously by Friswell et al 19 using the measured modal data.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Direct Versus Iterative Model Updating Methods for Mass and Stiffness Matrices

Yang

Chen

2010

Int. J. Str. Stab. Dyn.

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A comparative study is performed for the direct and iterative methods for updating the structural matrices based on measured data. The former was derived from the orthogonality constraints by replacing the modal vector of concern by the modal matrix in computing the correction matrices. 1 The iterative method used is the improved inverse eigensenstivity method. 2 Through the numerical studies, it was demonstrated that both methods yield good results. However, the direct updating method is found to be more suitable for engineering applications due to its ease in treating multi-modes and higher e±ciency, especially for complicated structures.

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“…Equations (19) or (20) su®er from the drawback that the updated matrix may not be symmetric. To remedy such a drawback, Eq.…”

Section: Generalization Of the Theory To Consider The¯rst Few Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Direct Versus Iterative Model Updating Methods for Mass and Stiffness Matrices

Yang

Chen

2010

Int. J. Str. Stab. Dyn.

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show abstract

“…Any of the previously discussed structures such as positive semi-definiteness or prescribed entries is allowable. In the literature, however, the most commonly discussed case is when M = M 0 ⪰ 0 and C and K are symmetric [5, 23, 28, 31]. The other slightly easier case is when C = C 0 = 0 [6, 12, 19, 43, 46].…”

Section: Model Updating Problemsmentioning

confidence: 99%

Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

2009

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In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or updating a vibration system from some observed or desirable dynamical behaviors while respecting some inherent feasibility constraints well suits many engineering applications. Thus far, however, QIEPs have remained challenging both theoretically and computationally due to the great variations of structural constraints that must be addressed. Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs.

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“…In the field of model updating, sometimes certain eigenvectors are required to satisfy some specific conditions [7, 8]. In all, only a few measured eigenvectors and eigenvalues are available [3, 9, 10, 11, 12]. It is more sensible and practically implementable to employ only the available, reliable, yet limited eigenpair information in the reconstruction or updating process.…”

Section: Introductionmentioning

confidence: 99%

Parameter reconstruction of vibration systems from partial eigeninformation

Dong

Lin

Chu

2009

Journal of Sound and Vibration

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Quadratic matrix polynomials are fundamental to vibration analysis. Because of the predetermined interconnectivity among the constituent elements and the mandatory nonnegativity of the physical parameters, most given vibration systems will impose some inherent structure on the coefficients of the corresponding quadratic matrix polynomials. In the inverse problem of reconstructing a vibration system from its observed or desirable dynamical behavior, respecting the intrinsic structure becomes important and challenging both theoretically and practically. The issue of whether a structured inverse eigenvalue problem is solvable is problem dependent and has to be addressed structure by structure. In an earlier work, physical systems that can be modeled under the paradigm of a serially linked mass-spring system have been considered via specifically formulated inequality systems. In this paper, the framework is generalized to arbitrary generally linked systems. In particular, given any configuration of interconnectivity in a mass-spring system, this paper presents a mechanism that systematically and automatically generates a corresponding inequality system. A numerical approach is proposed to determine whether the inverse problem is solvable and, if it is so, computes the coefficient matrices while providing an estimate of the residual error. The most important feature of this approach is that it is problem independent, that is, the approach is general and robust for any kind of physical configuration. The ideas discussed in this paper have been implemented into a software package by which some numerical experiments are reported.

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Direct Updating of Damping and Stiffness Matrices

Cited by 148 publications

References 13 publications

Direct Versus Iterative Model Updating Methods for Mass and Stiffness Matrices

Direct Versus Iterative Model Updating Methods for Mass and Stiffness Matrices

Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

Parameter reconstruction of vibration systems from partial eigeninformation

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