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An infinite dimensional model for a three-layer active constrained layer(ACL) beam model, consisting of a piezoelectric elastic layer at the top and anelastic host layer at the bottom constraining a viscoelastic layer in themiddle, is obtained for clamped-free boundary conditions by using a thoroughvariational approach. The Rao-Nakra thin compliant layer approximation isadopted to model the sandwich structure, and the electrostatic approach(magnetic effects are ignored) is assumed for the piezoelectric layer. Insteadof the voltage actuation of the piezoelectric layer, the piezoelectric layer isproposed to be activated by a charge (or current) source. We show that, theclosed-loop system with all mechanical feedback is shown to be uniformlyexponentially stable. Our result is the outcome of the compact perturbationargument and a unique continuation result for the spectral problem which relieson the multipliers method. Finally, the modeling methodology of the paper isgeneralized to the multilayer ACL beams, and the uniform exponentialstabilizability result is established analogously.

Modeling and stabilization results for a charge or current-actuated active constrained layer (ACL) beam model with the electrostatic assumption