The Construction of Physical Parameters From Modal Data

Burak, Senad; Ram, Yitshak M.

doi:10.1006/mssp.2000.1348

Cited by 10 publications

(10 citation statements)

References 9 publications

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“…We remark that it is not easy to find a set of positive parameters {m i } n 1 , {c i } n 1 and {k i } n 1 such that the corresponding matrices M, C, K satisfy Equation (7), see for instance [2,6,11] for the exploration of the physical solvability.…”

Section: Problem Formulationmentioning

confidence: 99%

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A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendata

Bai¹,

Ching²

2008

Numerical Linear Algebra App

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In this paper we consider an inverse problem for a damped vibration system from the noisy measured eigendata, where the mass, damping, and stiffness matrices are all symmetric positive definite matrices with the mass matrix being diagonal and the damping and stiffness matrices tridiagonal. To take into consideration the noise in the data, the problem is formulated as a convex optimization problem involving quadratic constraints on the unknown mass, damping, and stiffness parameters. Then we propose a smoothing Newtontype algorithm for the optimization problem, which improves a pre-existing estimate of a solution to the inverse problem. We show that the proposed method converges both globally and quadratically. Numerical examples are also given to demonstrate the efficiency of our method.

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Section: Problem Formulationmentioning

confidence: 99%

“…are satisfied, then it may result in three inaccurate estimates of M , C and K since the noise may be mixed up with the valuation of the matrices M , C and K. The real M , C and K will not satisfy exactly (6) for the noisy data. To overcome the problem, we will formulate the SIQEP with the partial noisy eigendata…”

Section: Introductionmentioning

confidence: 99%

A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendata

Bai¹,

Ching²

2008

Numerical Linear Algebra App

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“…Selected in the first example is a shear building model, primarily because this model has been studied recently by many researchers using various ad hoc updating approaches, often under a more strict assumption such as known mass matrices [5][6][7]. The second example, aimed at demonstrating the potential of the method for modelling large-scale industrial problems, considers a three-dimensional five-story frame structure, modelled as an 120-degree-of-freedom (DOF) system with 40 beam elements.…”

Section: Introductionmentioning

confidence: 99%

Cross-model cross-mode method for model updating

Wang

2007

Mechanical Systems and Signal Processing

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“…see [2,4,9,39] for the exploration of the physical solvability of the structured quadratic pencils. Moreover, we note that the eigendata…”

Section: Problem Reformulationmentioning

confidence: 99%

“…Our method is motivated by the recent development of the numerical computation for structured IQEPs and the BVI/NCP. Burak and Ram [4] constructed the structured pencil Q(λ) = λ 2 M + K with…”

Section: Mü(t) + Cu(t) + Ku(t)mentioning

confidence: 99%

Symmetric tridiagonal inverse quadratic eigenvalue problems with partial eigendata

Bai

2007

Inverse Problems

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In this paper we concern the inverse problem of constructing the n-by-n real symmetric tridiagonal matrices C and K so that the monic quadratic pencil Q(λ) := λ 2 I + λC + K (where I is the identity matrix) possesses the given partial eigendata. We first provide the sufficient and necessary conditions for the existence of an exact solution to the inverse problem from the self-conjugate set of prescribed four eigenpairs. To find a physical solution for the inverse problem where the matrices C and K are weakly diagonally dominant and have positive diagonal elements and negative off-diagonal elements, we consider the inverse problem from the partial measured noisy eigendata. We propose a regularized smoothing Newton method for solving the inverse problem. The global and quadratic convergence of our approach is established under some mild assumptions. Some numerical examples and a practical engineering application in vibrations show the efficiency of our method.

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The Construction of Physical Parameters From Modal Data

Cited by 10 publications

References 9 publications

A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendata

A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendata

Cross-model cross-mode method for model updating

Symmetric tridiagonal inverse quadratic eigenvalue problems with partial eigendata

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