Riesz Basis and Exponential Stability of a Variable Coefficients Rotating Disk-Beam-Mass System

2022 ◽  
Author(s):  
My Driss Aouragh ◽  
M’hamed Segaoui
Keyword(s):  
Exponential Stability ◽  
Riesz Basis ◽  
Rotating Disk ◽  
Variable Coefficients ◽  
Mass System

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 Exponential stability of a non-homogeneous rotating disk–beam–mass system

2015 ◽  
Vol 423 (2) ◽  
pp. 1243-1261 ◽  
Author(s):  
Xin Chen ◽  
Boumediene Chentouf ◽  
Jun-Min Wang
Keyword(s):  
Exponential Stability ◽  
Rotating Disk ◽  
Mass System

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.

Rotating Disk Shape: Is the Equation Nonlinear?

1989 ◽  
Vol 111 (4) ◽  
pp. 456-458
Author(s):  
R. R. Jettappa
Keyword(s):  
Differential Equation ◽  
Linear Equation ◽  
Rotating Disk ◽  
Variable Coefficients ◽  
Thin Disk ◽  
Second Order ◽  
First Order ◽  
Governing Differential Equation ◽  
Centrifugal Loading

The determination of the shape of a rotating disk under centrifugal loading is considered. It is shown that the governing differential equation for the shape of a rotating thin disk is reducible to a linear equation of second order with variable coefficients. However, the form of this equation is such that it can be treated as an equation of first order thereby facilitating the integration by quadratures. All this is possible without any additional mathematical assumptions so that the results are exact within the limitations of the thin disk theory.

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