Potential Formulation for Charge or Current-Controlled Piezoelectric Smart Composites and Stabilization Results: Electrostatic Versus Quasi-Static Versus Fully-Dynamic Approaches

Abstract

We consider a less-hysteretic piezoelectric smart composite beam model whose piezoelectric layers are actuated by charge or current only. The governing equations are derived through a consistent variational approach by the thin-compliant layer Rao–Nakra sandwich beam assumptions. For the inclusion of electromagnetic effects in piezoelectric layers, we consider all three approaches (electrostatic, quasi-static, and fully dynamic) of the potential formulation of Maxwell's equations. The initial value problems are shown to be well-posed by the Coulomb gauge condition. In the fully-dynamic approach, even though a dramatic reflection of magnetic effects on the stabilizability characteristics of the composite with the $B^*-$ type feedback is shown, the models provide alternate electromagnetic feedback controllers. In electrostatic and quasi-static approaches, exponential stability (charge) and asymptotic stability (current) results are proved. Finally, closed-loop systems for each approach and actuation are simulated by the filtered semidiscrete finite-difference method.