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

We consider a less-hysteretic piezoelectric smart composite beam whose piezoelectric layers are actuated by charge or current. The governing equations are derived through a consistent variational approach by the thin-compliant layer Rao-Nakra sandwich beam assumptions. For the inclusion of electro-magnetic effects in piezoelectric layers, we consider all three approaches (electrostatic, quasi-static and fully dynamic) of the potential formulation of Maxwell\u27s equations. Essentially, two sets of initial value problems (IVPs) are derived for each actuation: charge and current for each piezoelectric layer. The IVPs are shown to be well-posed with the choice of the Coulomb gauge condition. In fully-dynamic approaches, a dramatic reflection of magnetic effects on the stabilizability characteristics of the composite with the B^*−type feedback is shown. The corresponding models provide alternate electromagnetic state feedback controllers. In electrostatic and quasi-static approaches, exponential stability (charge) and asymptotic stability (current) results are proved. Finally, the stabilization results for each approach and actuation are simulated and compared side by sid