  A cantilevered piezoelectric smart composite beam, consisting of perfectly
bonded elastic, viscoelastic and piezoelectric layers, is considered. The
piezoelectric layer is actuated by a voltage source. Both fully dynamic and
electrostatic approaches, based on Maxwell's equations, are used to model the
piezoelectric layer. We obtain (i) fully-dynamic and electrostatic Rao-Nakra
type models by assuming that the viscoelastic layer has a negligible weight and
stiffness, (ii) fully-dynamic and electrostatic Mead-Marcus type models by
neglecting the in-plane and rotational inertia terms. Each model is a
perturbation of the corresponding classical smart composite beam model. These
models are written in the state-space form, the existence and uniqueness of
solutions are obtained in appropriate Hilbert spaces. Next, the stabilization
problem for each closed-loop system, with a thorough analysis, is investigated
for the natural $B^*-$type state feedback controllers. The fully dynamic
Rao-Nakra model with four state feedback controllers is shown to be not
asymptotically stable for certain choices of material parameters whereas the
electrostatic model is exponentially stable with only three state feedback
controllers (by the spectral multipliers method). Similarly, the fully dynamic
Mead-Marcus model lacks of asymptotic stability for certain solutions whereas
the electrostatic model is exponentially stable by only one state feedback
controller.stable by one feedback controller applied to the bending moment
only.
