Oscillations of a temperature-dependent piezoelectric rod

TL;DR

This paper develops a thermodynamically consistent model for piezoelectric materials that accounts for hysteresis, heat production, and temperature effects, providing analytical proof of solution existence for the coupled PDE system.

Contribution

It introduces a novel phenomenological model incorporating temperature-dependent hysteresis and feedback effects in piezoelectric materials, with proven solution existence.

Findings

Model is thermodynamically consistent

Existence of solutions for the PDE system is proven

Inverse Preisach operator with temperature-dependent density is used

Abstract

Piezoelectricity of some materials has shown to have many applications, in particular in energy harvesting. Due to the inherent hysteresis in the characteristic of such materials, a number of hysteretic models have been proposed minding the fact that hysteresis losses may influence the efficiency of the process. However, hysteresis dissipation is accompanied with heat production, which in turn increases the temperature of the device and may change its physical characteristics. In this paper we propose a phenomenological model for electromechanical coupling in piezoelectric materials where temperature and feedback effects are taken into account. We prove the existence of solution for the resulting PDE system and show that the model is thermodynamically consistent. The main analytical tool is the inverse Preisach operator with temperature-dependent density.