Geodesic
Riesz basis and exponential stability for Euler-Bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This article concerns the Riesz basis property and the stability of a damped Euler-Bernoulli beam with nonuniform thickness or density, that is clamped at one end and is free at the other. To stabilize the system, we apply a linear boundary control force in position and velocity at the free end of the beam. We first put some basic properties for the closed-loop system and then analyze the spectrum of the system. Using the modern spectral analysis approach for two-points parameterized ordinary differential operators, we obtain the Riesz basis property. The spectrum-determined growth condition and the exponential stability are also concluded.
Classification : 93C20, 93D15, 35B35, 35P10
Keywords: beam equation, asymptotic analysis, Riesz basis, exponential stability 
@article{EJDE_2015__2015__a0,
     author = {Tour\'e, K.Augustin and Coulibaly, Adama and Hermith Kouassi, Ayo A.},
     title = {Riesz basis and exponential stability for {Euler-Bernoulli} beams with variable coefficients and indefinite damping under a force control in position and velocity},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a0/}
}
TY  - JOUR
AU  - Touré, K.Augustin
AU  - Coulibaly, Adama
AU  - Hermith Kouassi, Ayo A.
TI  - Riesz basis and exponential stability for Euler-Bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity
JO  - Electronic Journal of Differential Equations
PY  - 2015
VL  - 2015
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a0/
LA  - en
ID  - EJDE_2015__2015__a0
ER  - 
%0 Journal Article
%A Touré, K.Augustin
%A Coulibaly, Adama
%A Hermith Kouassi, Ayo A.
%T Riesz basis and exponential stability for Euler-Bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity
%J Electronic Journal of Differential Equations
%D 2015
%V 2015
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a0/
%G en
%F EJDE_2015__2015__a0
Touré, K.Augustin; Coulibaly, Adama; Hermith Kouassi, Ayo A. Riesz basis and exponential stability for Euler-Bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a0/