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

TL;DR

This paper develops an infinite-dimensional model for a three-layer ACL beam with charge or current actuation, demonstrating uniform exponential stability of the closed-loop system under mechanical feedback, using variational methods and spectral analysis.

Contribution

It introduces a novel charge/current actuation approach for ACL beams and proves their exponential stabilization, extending the modeling to multilayer structures.

Findings

The closed-loop system is uniformly exponentially stable.

The modeling approach is generalized to multilayer ACL beams.

Stability proof uses compact perturbation and spectral methods.

Abstract

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.