Journal of Applied Mathematics

A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping

Xin Yu, Zhigang Ren, Qian Zhang, and Chao Xu

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Abstract

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.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 982574, 7 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305846

Digital Object Identifier
doi:10.1155/2014/982574

Mathematical Reviews number (MathSciNet)
MR3228147

Citation

Yu, Xin; Ren, Zhigang; Zhang, Qian; Xu, Chao. A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping. J. Appl. Math. 2014 (2014), Article ID 982574, 7 pages. doi:10.1155/2014/982574. https://projecteuclid.org/euclid.jam/1425305846


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