Modeling and controlling an active constrained layer (ACL) beam actuated by two voltage sources with/without magnetic effects

TL;DR

This paper models a three-layer ACL beam with magnetic effects and voltage actuation, analyzing stability and control properties under different assumptions and boundary conditions.

Contribution

It introduces a comprehensive dynamic model of an ACL beam including magnetic effects and compares stability outcomes with electrostatic assumptions.

Findings

Magnetic effects influence stabilization outcomes.

Electrostatic assumption yields exponential stability.

Certain parameter regimes prevent uniform stabilization.

Abstract

A fully dynamic three-layer active constrained layer (ACL) beam is modeled for cantilevered boundary conditions by using a thorough variational approach. The Rao-Nakra thin compliant layer assumptions are adopted to model the sandwich structure, and all magnetic effects for the piezoelectric layers are retained. The piezoelectric layers are activated by two different voltage sources. When there are no "mechanical" boundary forces acting in the longitudinal direction, it is shown that the system with certain parameter combinations is not uniformly strongly stabilizable by the $B^*-$type feedback controller, which is the total current accumulated at the electrodes for the piezoelectric layers. However, as the magnetic effects are ignored (electrostatic assumption), the closed-loop system with all mechanical feedback controllers is shown to be uniformly exponentially stable.