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

Abstract

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's 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 side

Disciplines

Acoustics, Dynamics, and Controls | Applied Mathematics | Applied Mechanics | Engineering Science and Materials | Mechanics of Materials

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