The local stability of oscilation problems to differents models of beams

In this talk we a introduce local dissipative mechanism able to produce exponential sta- bility. We will show that under some conditions no matter the quantity of dissipative mechanis we can introduce, the corresponding system is never exponentially stable. We will show situation that even there is a lack of polynomial stability. On the other hand, de- pending on the position, the material, and the dissipative mechanism, we will show some condition for which the local dissipative mechanism is effective and produce exponential stability of the system. We show some examples and applications.