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2014 A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping
Xin Yu, Zhigang Ren, Qian Zhang, Chao Xu
J. Appl. Math. 2014: 1-7 (2014). DOI: 10.1155/2014/982574

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.

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Xin Yu. Zhigang Ren. Qian Zhang. Chao Xu. "A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping." J. Appl. Math. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/982574

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07132033
MathSciNet: MR3228147
Digital Object Identifier: 10.1155/2014/982574

Rights: Copyright © 2014 Hindawi

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