Luci Fatori, Tais De Olivera Saito, Mauricio Sepúlveda, Eiji Renan Takahashi:
Energy decay to Timoshenko system with indefinite damping
We consider the classical Timoshenko system for vibrations of thin rods. The system has an indenite damping mechanism, i.e. it has a damping function a = a(x) possibly changing sign, present only in the equation for the vertical displacement. We shall prove that exponential stability depends on conditions regarding of the indenite damping function a and a nice relationship between the coecient of the system. Finally, we give some numerical result to verify our analytical results.