Stabilisation exponentielle d’une équation des poutres d’Euler-Bernoulli à coefficients variables

Aouragh, My Driss; Yebari, Naji

doi:10.5802/ambp.275

Cited by 2 publications

(9 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e analysis of the graphical results allowed us to affirm that the control in velocity allows the beam to stabilize faster than when the control is done in displacement. is result, which we confirmed after a statistical study of the sensitivity of the control parameters, corroborates that obtained in the numerical study of the spectrum of the operator associated with the model by Aouragh and Yebari in [7] and later by Kouassi et al in [2].…”

Section: Discussionsupporting

confidence: 91%

Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity

Brahima

Narcisse

Adou

2022

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

Our model is based on an Euler-Bernoulli beam clamped at one end and subjected at its free end to a control in displacement and velocity. In this work, relative of the control parameters, we study the stabilization in displacement and then in energy of the model using a stable numerical scheme that we implement. This numerical scheme results from the Crank–Nicolson algorithm for the discretization in time and from the finite element method based on the approximation by Hermith cubic functions for the discretization in space. The study shows that, compared to the velocity control, the displacement control has an almost negligible effect on the stabilization of the beam. This result is confirmed later by a sensitivity study on the control parameters involved in our model.

show abstract

Section: Discussionsupporting

confidence: 91%

Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity

Brahima

Narcisse

Adou

2022

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…Here, first, we find a general asymptotic expression of the eigenvalues of the system where we could deduce those found by Jean-Marc et al [6] and Aouragh and Yebari [1] in the constant case. Next, by proceeding by Wang [7], the exponential stability of the system (1) is obtained when γ is non-negative in [0,1], and we discuss the case that γ is continuous and indefinite on the interval [0, 1].…”

Section: Introductionsupporting

confidence: 77%

“…This present work reveals capital importance because it is a general case of the results obtained in several works [1][2][3][4][5][6].…”

Section: Introductionsupporting

confidence: 59%

“…Aouragh and Yebari [1] studied the system (1) without damping (γ ¼ 0) and with the condition ζ 12 >0. In their article, the authors showed that there is a sequence of generalized eigenfunctions that form a Riesz basis of the appropriate Hilbert space and that there is exponential stability under certain conditions relating to the feedback coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…For our part, we study the system (1) with the presence of a viscous damping γ x ð Þ>0 and the condition ζ 12 ≥ 0. To do this, we analyze two situations as follows:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Study of the Stability Properties for a General Shape of Damped Euler–Bernoulli Beams under Linear Boundary Conditions

Kouakou Kra Isaac,

Gossrin Jean-Marc,

Kidjegbo Augustin

et al. 2023

Abstract and Applied Analysis

View full text Add to dashboard Cite

We study in this paper a general shape of damped Euler–Bernoulli beams with variable coefficients. Our main goal is to generalize several works already done on damped Euler–Bernoulli beams. We start by studying the spectral properties of a particular case of the system, and then we determine asymptotic expressions that generalize those obtained by other authors. At last, by adopting well-known techniques, we establish the Riesz basis property of the system in the general case, and the exponential stability of the system is obtained under certain conditions relating to the feedback coefficients and the sign of the internal damping on the interval studied of length 1 .

show abstract

Stabilisation exponentielle d’une équation des poutres d’Euler-Bernoulli à coefficients variables

Cited by 2 publications

References 4 publications

Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity

Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity

Study of the Stability Properties for a General Shape of Damped Euler–Bernoulli Beams under Linear Boundary Conditions

Contact Info

Product

Resources

About