On modelling and stabilizability of current-controlled piezoelectric material

TL;DR

This paper introduces a new dynamic electromagnetic model for current-controlled piezoelectric composites using combined Lagrangian methods, analyzing their stabilizability with electric feedback across different beam theories.

Contribution

It develops well-posed, fully dynamic models for piezoelectric composites based on Euler-Bernoulli and Timoshenko theories, and demonstrates their asymptotic stabilizability via simple electric feedback.

Findings

Models are mathematically well-posed.

Systems are asymptotically stabilizable.

Passive system behavior under electric feedback.

Abstract

This paper presents a new modelling approach to fully dynamic electromagnetic current-controlled piezoelectric composite models that require a combined Lagrangian. To model the mechanical domains, we consider two different beam theories, i.e. the Euler-Bernoulli and Timoshenko beam theories. We show that both derived piezoelectric composite models are well-posed. Furthermore, we show through analysis and simulations that both current-controlled piezoelectric composites are asymptotically stabilizable through simple electric feedback, which renders the system passive in a classical way for certain system parameters. In this work, we also review several related piezoelectric beams, actuators, and composite models.