On modelling and stabilizability of voltage-controlled piezoelectric material

TL;DR

This paper introduces new models for voltage-controlled piezoelectric materials, analyzes their well-posedness, and demonstrates conditions under which the systems are stabilizable, advancing understanding of piezoelectric system control.

Contribution

It presents novel piezoelectric actuator and composite models, establishes their well-posedness, and identifies stabilizability conditions for specific parameters.

Findings

Piezoelectric composite is stabilizable under certain parameters.

New definitions for electromagnetic considerations in piezoelectric systems.

Models are proven to be well-posed.

Abstract

In this paper, we present a new piezoelectric actuator and piezoelectric composite model and show the well-posedness of these systems. Furthermore, we show that the piezoelectric composite is stabilizable for certain system parameters. In this work, we also review several piezoelectric beams, actuators, and composite models and provide improved definitions of the different electromagnetic considerations, i.e. fully dynamic electromagnetic field, quasi-static electric field, and the static lectric field assumption.