scholarly journals Exponential decay rate for a wave equation with Dirichlet boundary control

2007 ◽  
Vol 20 (8) ◽  
pp. 861-865 ◽  
Author(s):  
Chuanxian Deng ◽  
Yan Liu ◽  
Weisheng Jiang ◽  
Falun Huang
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Boundary Control ◽  
Exponential Decay ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Control ◽  
Exponential Decay Rate

scholarly journals The operatorB*Lfor the wave equation with Dirichlet control

2004 ◽  
Vol 2004 (7) ◽  
pp. 625-634 ◽  
Author(s):  
I. Lasiecka ◽  
R. Triggiani
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Arbitrary Dimension ◽  
Energy Methods ◽  
Smooth Bounded Domain ◽  
Dirichlet Boundary Control

In the case of the wave equation, defined on a sufficiently smooth bounded domain of arbitrary dimension, and subject to Dirichlet boundary control, the operatorB*Lfrom boundary to boundary is bounded in theL2-sense. The proof combines hyperbolic differential energy methods with a microlocal elliptic component.

Lyapunov-Based Boundary Control of Strain Gradient Microscale Beams With Exponential Decay Rate

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Ramin Vatankhah ◽  
Ali Najafi ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Decay Rate ◽  
Boundary Control ◽  
Exponential Decay ◽  
Strain Gradient ◽  
Beam Element ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Exponential Decay Rate ◽  
Mass Matrices ◽  
Euler Bernoulli Beam

In nonclassical microbeams, the governing partial differential equation (PDE) of the system and corresponding boundary conditions are obtained based on the nonclassical continuum mechanics. In this study, exponential decay rate of a vibrating nonclassical microscale Euler–Bernoulli beam is investigated using a linear boundary control law and by implementing a proper Lyapunov functional. To illustrate the performance of the designed controllers, the closed-loop PDE model of the system is simulated via finite element method (FEM). To this end, new nonclassical beam element stiffness and mass matrices are developed based on the strain gradient theory and verification of this new beam element is accomplished in this work.

Sign in / Sign up

Export Citation Format

Share Document