Ali Wehbe
Title :
Polynomial stability of Timoshenko beam by one locally distributed feedback
Abstract :
In this paper, we study the energy decay rate for an elastic Timoshenko system. The system
consists of two coupled wave equations. Only the equation about the rotation angle is
damped by one locally distributed feedback at the neighborhood of the boundary. The
equation for the transverse displacement of the beam is only indirectly damped through
the coupling.
First, we establish an exponential energy decay rate in the case of the same speed of
propagation. Next, when the wave speeds are different, a polynomial type decay rate is
obtained. These results are proved by verifying the frequency domain conditions.