On the general governing equations of electromagnetic acoustic transducers

TL;DR

This paper derives comprehensive governing equations combining electromagnetism and continuum mechanics to model electromagnetic acoustic transducers, accounting for complex factors like finite deformations and thermal effects.

Contribution

It introduces a unified mathematical framework for EMATs that includes nonlinear elasticity, thermal effects, and incremental boundary conditions, advancing modeling accuracy.

Findings

Unified equations for EMATs considering nonlinear elasticity.

Inclusion of thermal effects and heat generation in models.

Framework for solving wave propagation boundary value problems.

Abstract

In this paper, we present the general governing equations of electrodynamics and continuum mechanics that need to be considered while mathematically modelling the behaviour of electromagnetic acoustic transducers (EMATs). We consider the existence of finite deformations for soft materials and the possibility of electric currents, temperature gradients, and internal heat generation due to dissipation. Starting with Maxwell's equations of electromagnetism and balance laws of nonlinear elasticity, we present the governing equations and boundary conditions in incremental form in order to solve wave propagation problems of boundary value type.