Theoretical and numerical aspects related to the energy of some Timoshenko systems

We recall in this note some recent results concerning the Timoshenko system which is here subject to different types of dissipation (undamped, linear damping and nonlinear damping). More precisely, the emphasis will be on the behavior, for a time large enough, of the energy associated with the solution of the damped Timoshenko system. We numerically confirm the conservation property and the theoretical results established on the decay rates of the energy associated with each type of dissipation.