On modelling and stabilizability of current-controlled piezoelectric material

2023/09/06 by de Jong, Matthijs C., Scherpen, Jacquelien M. A.
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)

paper · doi:10.48550/arxiv.2310.06849

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.

Related

• On modelling and stabilizability of voltage-controlled piezoelectric material
• Novel current actuated piezoelectric composite model with fully dynamic electromagnetic field
• Modeling and related results for current-actuated piezoelectric beams by including magnetic effects
• Modeling and stabilization results for a charge or current-actuated active constrained layer (ACL) beam model with the electrostatic assumption
• The Exponential Stabilization of a Heat and Piezoelectric Beam Interaction with Static or Hybrid Feedback Controllers