Paper Info
Title
A Numerical Method of the Euler-Bernoulli Beam with Optimal Local Kelvin-Voigt Damping.
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.
Year
DOI
Venue
2014
10.1155/2014/982574
JOURNAL OF APPLIED MATHEMATICS
Field
DocType
Volume
Mathematical optimization,Nonlinear system,Optimal control,Parametrization,Mathematical analysis,Finite element method,Euler's formula,Beam (structure),Numerical analysis,Mathematics,Bernoulli's principle
Journal
2014
ISSN
Citations 
PageRank 
1110-757X
0
0.34
References 
Authors
7
4
Name
Order
Citations
PageRank
Xin Yu151.51
Zhigang Ren2213.97
Qian Zhang329043.11
Chao Xu413633.20