  An infinite dimensional model for a three-layer active constrained layer
(ACL) beam model, consisting of a piezoelectric elastic layer at the top and an
elastic host layer at the bottom constraining a viscoelastic layer in the
middle, is obtained for clamped-free boundary conditions by using a thorough
variational approach. The Rao-Nakra thin compliant layer approximation is
adopted to model the sandwich structure, and the electrostatic approach
(magnetic effects are ignored) is assumed for the piezoelectric layer. Instead
of the voltage actuation of the piezoelectric layer, the piezoelectric layer is
proposed to be activated by a charge (or current) source. We show that, the
closed-loop system with all mechanical feedback is shown to be uniformly
exponentially stable. Our result is the outcome of the compact perturbation
argument and a unique continuation result for the spectral problem which relies
on the multipliers method. Finally, the modeling methodology of the paper is
generalized to the multilayer ACL beams, and the uniform exponential
stabilizability result is established analogously.
