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A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping
Joint Authors
Zhang, Qian
Ren, Zhigang
Yu, Xin
Xu, Chao
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-30
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints.
The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal.
We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system.
Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm.
At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam.
American Psychological Association (APA)
Yu, Xin& Ren, Zhigang& Zhang, Qian& Xu, Chao. 2014. A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-513406
Modern Language Association (MLA)
Yu, Xin…[et al.]. A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping. Journal of Applied Mathematics No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-513406
American Medical Association (AMA)
Yu, Xin& Ren, Zhigang& Zhang, Qian& Xu, Chao. A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-513406
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-513406