Mathematical justification of stabilized 2D piezoelectric plates with electromagnetic feedback

Munyabugingo  Valens; Banzi  Wellars; Abdou  Sène

doi:10.59400/adecp4298

Mathematical justification of stabilized 2D piezoelectric plates with electromagnetic feedback

Munyabugingo Valens
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali P.O. Box 3900, Rwanda;

Department of Mathematics and Computer Science Education, School of Mathematics and Science Education, College of Education, University of Rwanda, Rwamagana P.O. Box 55, Rwanda
Banzi Wellars
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali P.O. Box 3900, Rwanda
Abdou Sène
Pôle d’Innovation et d’Expertise pour le Développement (PIED), Université Numérique Cheikh Hamidou Kane (UNCHK), Fann, Dakar BP 15126, Sénégal

Article ID: 4298

DOI: https://doi.org/10.59400/adecp4298

Keywords: piezoelectricity; asymptotic analysis; scaling; feedback control

Abstract

In this paper, we provide a rigorous mathematical justification for a simplified model of a piezoelectric plate stabilized around a steady state. Asymptotic analysis of a 3D piezoelectric materials model with linear feedback control laws is performed as the thickness h of the plate tends to zero. We derive a 2D piezoelectric plate model which is consistent and stable for an approximation of the 3D model, ensuring its validity for the design of thin electromechanical devices. The energy decay for the 2D and 3D systems is established. Such a dimension reduction is very important because, when the plate thickness is very small, it simplifies numerical calculations and, above all, avoids the numerical calculation problems caused by distortion between the plate dimensions. Furthermore, the study reveals that when the thickness of a piezoelectric plate is very small, we no longer need the restrictions to only eleven stabilizable types of piezoelectric materials. The core contribution of this work is the direct integration of this fully coupled dimensional reduction with control theory.

Published

2026-06-23

How to Cite

Valens, M., Wellars, B., & Sène, A. (2026). Mathematical justification of stabilized 2D piezoelectric plates with electromagnetic feedback. Advances in Differential Equations and Control Processes, 33(2). https://doi.org/10.59400/adecp4298

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Issue

Vol. 33 No. 2 (2026)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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