Physical parameters reconstruction of a fixed–fixed mass-spring system from its characteristic data

Huang, Xiantong; Hu, Xi-Yan; Zhang, Lei

doi:10.1016/j.cam.2006.08.011

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Recently, some new results have been obtained on the inverse eigenvalue problems for Jacobi matrices, see [1][2][3][4]. Using two sets of eigenvalues or two incomplete eigenpairs, the inverse vibration problems of spring-mass systems have been studied by Nylen and Uhlig [5], and Huang, et al [6]. Bai [7], and Tian and Dai [8] considered by one eigenpair or two eigenpairs to determine spring-mass systems, and proposed numerical algorithms for solving the problems.…”

Section: Introductionmentioning

confidence: 99%

The Reconstruction of Spring-Mass System with Partial Given Data

Wen-ting¹

2016

Proceedings of the 2015 International Conference on Mechanical Science and Engineering

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In this paper, two inverse vibration problems of constructing a grounding spring-mass system from its two eigenpairs and part of spring stiffness are considered. The vibration system is constrained to satisfy a relation that the total mass of system is a constant, and the problems are transferred into inverse eigenvalue problems for Jacobi matrix. The necessary and sufficient conditions for the construction of physically realizable systems with positive parameters are derived. Furthermore, the corresponding numerical algorithms and numerical example are given.

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Section: Introductionmentioning

confidence: 99%

The Reconstruction of Spring-Mass System with Partial Given Data

Wen-ting¹

2016

Proceedings of the 2015 International Conference on Mechanical Science and Engineering

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“…In recent years, some new results have been obtained on the construction of a Jacobi matrix, see [1] [2][3] [4]. Using two sets of eigenvalues or two incomplete eigenpairs, the inverse eigenvalue problems have been studied [5][6] [7]. Problems [8][9] [10] have been solved by one eigenpair or two eigenpairs to determine corresponding systems, and numerical algorithms for solving the problems were proposed.…”

Section: Introductionmentioning

confidence: 99%

Parameter Reconstruction of a Circuit System from Partial Eigeninformation

Wen-ting

2018

J. Phys.: Conf. Ser.

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Abstract. In this paper, the inverse eigenvalue problem of reconstructing a LC circuit system from its some parameters and incomplete eigenpairs is considered. The necessary and sufficient condition for the solvability of the problem is derived by solving a kind of general inverse eigenvalue problems. The computational expressions of the solution, the related numerical algorithm and a numercical example are given.

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“…. , m n } and Recently, new spectral information to reconstruct the system (M n , K n ) have been considered by Huang et al in [7]:…”

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confidence: 99%

Extreme spectra realization by real symmetric tridiagonal and real symmetric arrow matrices

Pickmann¹,

Na²,

Soto³

2011

ELA

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Abstract. We consider the following two problems: to construct a real symmetric arrow matrix A and to construct a real symmetric tridiagonal matrix A, from a special kind of spectral information: one eigenvalue λ (j) of the j ×j leading principal submatrix A j of A, j = 1, 2, . . . , n; and one eigenpairHere we give a solution to the first problem, introduced in [J. Peng, X.Y. Hu, and L. Zhang. Two inverse eigenvalue problems for a special kind of matrices. Linear Algebra Appl., 416:336-347, 2006.]. In particular, for both problems to have a solution, we give a necessary and sufficient condition in the first case, and a sufficient condition in the second one. In both cases, we also give sufficient conditions in order that the constructed matrices be nonnegative. Our results are constructive and they generate algorithmic procedures to construct such matrices.

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Physical parameters reconstruction of a fixed–fixed mass-spring system from its characteristic data

Cited by 4 publications

References 14 publications

The Reconstruction of Spring-Mass System with Partial Given Data

The Reconstruction of Spring-Mass System with Partial Given Data

Parameter Reconstruction of a Circuit System from Partial Eigeninformation

Extreme spectra realization by real symmetric tridiagonal and real symmetric arrow matrices

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