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 eAt 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).

Año de publicación:

2015

Keywords:

• Timoshenko's beam
• Essential radius
• Uniform stabilization
• Semigroup theory
• Polynomial decay
• Tip body

Fuente:

scopus