Dynamic Equation in Thermo-piezoelectric Dissipative Media from Energy Conservation

TL;DR

This paper introduces an energy conservation-based methodology for deriving dynamic equations in thermo-piezoelectric dissipative media, offering a simpler and more versatile alternative to Hamiltonian approaches, especially for dissipative and multi-physical systems.

Contribution

The paper presents a novel energy conservation framework for formulating dynamic equations in dissipative media, extending applicability to complex multi-physical interactions.

Findings

Formulations agree with Hamiltonian principle results.

Framework effectively handles dissipation in thermo-piezoelectric media.

Potential extension to electrodynamics, fluid mechanics, and quantum mechanics.

Abstract

A methodology is proposed for formulating dynamic equations in thermo-piezoelectric and dissipative media from the first principle of energy conservation. The results are in agreement with those from Hamiltonian principle. Our formulations based on energy conservation are much easier to understand. What is more is that, the energy conservation based framework is able to handle dissipation problems, which is usually behind the scope of Hamiltonian principle. In our case, the mechanical, electric and thermal phenomena firstly are taken into account, and then the medium with dissipation is included. The formulations on acoustic dynamic equation and the associated constitutive relations of the medium will also pave an alternative way in computational dynamic modelling based on weak formulations. In addition, our methodology may be extended to other dynamic equation formulations, such as in electrodynamics, fluid mechanics and quantum mechanics. This is especially true for tackling the problems with multi-physical field interactions and coupling.