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 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 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. 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 electro-magnetic 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 semi-discrete Finite Difference method.

Disciplines

Applied Mathematics | Dynamical Systems | Electrical and Computer Engineering | Engineering | Engineering Science and Materials | Materials Science and Engineering | Mechanical Engineering | Nanoscience and Nanotechnology

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