ON THE NUMERICAL APPROXIMATION OF THE SPECTRUM OF A FLEXIBLE EULER-BERNOULLI BEAM WITH A FORCE CONTROL IN VELOCITY AND A MOMENT CONTROL IN ROTATING VELOCITY

2020 ◽  
Vol 126 (1) ◽  
pp. 13-31
Author(s):  
Mensah E. Patrice
Keyword(s):  
Force Control ◽  
Numerical Approximation ◽  
Bernoulli Beam ◽  
Moment Control ◽  
Euler Bernoulli Beam

scholarly journals Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation

2017 ◽  
Vol 9 (6) ◽  
pp. 1
Author(s):  
Bomisso G. Jean Marc ◽  
Tour\'{e} K. Augustin ◽  
Yoro Gozo
Keyword(s):  
Exponential Stability ◽  
Force Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Variable Coefficients ◽  
Viscous Damping ◽  
Closed Loop System ◽  
Bernoulli Beam ◽  
Spectral System ◽  
Euler Bernoulli Beam

This paper investigates the problem of exponential stability for a damped Euler-Bernoulli beam with variable coefficients clamped at one end and subjected to a force control in rotation and velocity rotation. We adopt the Riesz basis approach for show that the closed-loop system is a Riesz spectral system. Therefore, the exponential stability and the spectrum-determined growth condition are obtained.

scholarly journals Dissipative Numerical Method for a Flexible Euler-Bernoulli Beam with a Force Control in Rotation and Velocity Rotation

2017 ◽  
Vol 9 (4) ◽  
pp. 30
Author(s):  
Bomisso G. Jean Marc ◽  
Tour\'{e} K. Augustin ◽  
Yoro Gozo
Keyword(s):  
Force Control ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Second Step ◽  
Bernoulli Beam ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Priori Error Estimates ◽  
Nicolson Scheme ◽  
Euler Bernoulli Beam

In this paper, we study a flexible Euler-Bernoulli beam clamped at one end and subjected to a force control in rotation and velocity rotation. We develop a finite element method, stable and convergent which preserves the property of time decay of energy in the continuous case. We prove firstly the existence and uniqueness of the weak solution. Then, we discretize the system in two steps: in the first step, a semi-discrete scheme is obtained for discretization in space and, in the second step, a fully-discrete scheme is obtained for discretization in time by the Crank-Nicolson scheme. At each step of the discretization, the a-priori error estimates are obtained.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xin Yu ◽  
Zhigang Ren ◽  
Qian Zhang ◽  
Chao Xu
Keyword(s):  
Control Problem ◽  
Numerical Approximation ◽  
Optimal Parameter ◽  
Nonlinear Coefficient ◽  
Programming Algorithm ◽  
Beam Equation ◽  
Control Input ◽  
Bernoulli Beam ◽  
Finite Dimensional ◽  
Euler Bernoulli Beam

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.

LMI-based hybrid temporal-spatial differential control design for a class of Euler-Bernoulli beam system

2021 ◽  
pp. 095440622110036
Author(s):  
Jiaqi Zhong ◽  
Xiaolei Chen ◽  
Yupeng Yuan ◽  
Jiajia Tan
Keyword(s):  
Vibration Suppression ◽  
Direct Method ◽  
Recursive Algorithm ◽  
Linear Matrix ◽  
Bernoulli Beam ◽  
Hybrid Controller ◽  
Beam System ◽  
Active Vibration ◽  
Differential Control ◽  
Euler Bernoulli Beam

This paper addresses the problem of active vibration suppression for a class of Euler-Bernoulli beam system. The objective of this paper is to design a hybrid temporal-spatial differential controller, which is involved with the in-domain and boundary actuators, such that the closed-loop system is stable. The Lyapunov’s direct method is employed to derive the sufficient condition, which not only can guarantee the stabilization of system, but also can improve the spatial cooperation of actuators. In the framework of the linear matrix inequalities (LMIs) technology, the gain matrices of hybrid controller can obtained by developing a recursive algorithm. Finally, the effectiveness of the proposed methodology is demonstrated by applying a numerical simulation.

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