scholarly journals Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients

2002 ◽  
Vol 40 (6) ◽  
pp. 1905-1923 ◽  
Author(s):  
Bao-Zhu Guo
Keyword(s):  
Exponential Stability ◽  
Riesz Basis ◽  
Basis Property ◽  
Variable Coefficients ◽  
Bernoulli Beam ◽  
Riesz Basis Property ◽  
Beam Equations ◽  
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.

Riesz Basis Generation of the Euler-Bernoulli Beam Equation with Boundary Energy Dissipation

2012 ◽  
Vol 433-440 ◽  
pp. 123-127
Author(s):  
Cui Lian Zhou
Keyword(s):  
Energy Dissipation ◽  
Boundary Conditions ◽  
Riesz Basis ◽  
Boundary Energy ◽  
Basis Property ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Riesz Basis Property ◽  
Euler Bernoulli Beam ◽  
Regular Property

In this paper, the Riesz basis generation of the Euler-Bernoulli beam equation with with boundary energy dissipation is studied. Using the regular property of the boundary conditions, it is shown that the Riesz basis property holds

scholarly journals Riesz basis property and exponential stability for one-dimensional thermoelastic system with variable coefficients

2021 ◽  
Author(s):  
Bao-Zhu Guo ◽  
Han-Jing Ren
Keyword(s):  
Exponential Stability ◽  
Riesz Basis ◽  
Basis Property ◽  
Coupled System ◽  
Variable Coefficients ◽  
Operator Pencil ◽  
Riesz Basis Property ◽  
Asymptotic Expressions ◽  
The Matrix ◽  
Constant Coefficients

In this paper, we study Riesz basis property and stability for a nonuniform thermoelastic system with Dirichlet-Dirichlet boundary condition, where the  heat subsystem is considered as a control to the whole coupled system. By means of the matrix operator pencil method, we obtain the asymptotic expressions of the eigenpairs, which are exactly coincident to the constant coefficients case} We then show that there exists a sequence of generalized eigenfunctions of the system,  which forms a Riesz basis for the state space and the spectrum determined growth condition is therefore proved. As a result, the exponential stability of the system is concluded.

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