The hybrid-penalized method for the Timoshenko's beam

In this paper we introduce the hybrid-penalized method, to show the global existence of at least one solution to the Signorini's problem for a Timoshenko Beam. The main advantage of this method is that we can improve all result about asymptotic behaviour to contact problem to any boundary conditions, which is not possible with multiplicative techniques. Moreover this method also allows us to show polynomial stability to partial dissipative models. Finally, we performed numerical experiments to highlight our theoretical results.