Rates of decay to non homogeneous Timoshenko model with tip body

Abstract We consider the uniform stabilization of a hybrid elastic model consisting of a Timoshenko beam and a tip load at the free end of the beam. Our main result proves that the semigroup e A t associated to this model is not exponentially stable. Moreover, we prove that the semigroup decays polynomially to zero as t − 1 / 2 . When the damping mechanism is effective only on the boundary of the rotational angle, the solution also decays polynomially as t − 1 / 2 provided the wave speeds are equal. Otherwise it decays as t − 1 / 4 for any initial data taken in D ( A ) .