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

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 $B^{\ast }-$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.

References in corpus (4)

• Modeling and stabilizability of voltage-actuated piezoelectric beams with magnetic effects
• Further stabilization results for voltage-actuated piezoelectric beams with magnetic effects
• Exact boundary controllability results for a multilayer Rao-Nakra sandwich beam
• Uniform stabilization of a multilayer Rao-Nakra sandwich beam

Cited by in corpus (4)

• Modeling and semigroup formulation of charge or current-controlled active constrained layer (ACL) beams; electrostatic, quasi-static, and fully-dynamic assumptions
• Exponential Stability and Design of Sensor Feedback Amplifiers for Fast Stabilization of Magnetizable Piezoelectric Beam Equations
• Nonlinear modeling and preliminary stabilization results for a class of piezoelectric smart composite beams
• Exponential stabilization of a smart piezoelectric composite beam with only one boundary controller