热压电耗散介质的能量守恒动力学方程
Dynamic Equation in Thermo-piezoelectric Dissipative Media from Energy Conservation
摘要：
从能量守恒第一性原理出发，提出了一种建立热压电耗散介质动力学方程的方法。所得结果与哈密顿原理所得结果一致。我们基于能量守恒的公式更容易理解。更重要的是，基于能量守恒的框架能够处理耗散问题，这通常是落后于哈密顿原理的范围。在我们的例子中，首先考虑的机械，电气和热的现象，然后包括与耗散介质。声动力学方程和介质本构关系的建立也为基于弱公式的计算动力学建模提供了一条新的途径。此外，我们的方法可以扩展到其他动力学方程公式，如电动力学，流体力学和量子力学。这对于处理多物理场相互作用和耦合的问题尤其如此。
英文摘要：
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.
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