AI 中文总结
本研究基于全局能量守恒构建各向异性多相多孔压电介质的弹性动力学方程，消除虚拟质量参数，保证热力学自洽性，退化为经典理论，通过数值计算揭示机电耦合特性。
AI 中文摘要
多相多孔压电介质是先进换能器和智能传感器的核心材料。现有理论通常为每一相假设牛顿第二定律，或依赖现象学哈密顿量构建；前者需特设虚拟质量张量来描述相间惯性，后者在压电与多相耦合叠加时无法从根本上避免热力学不一致性。本研究从全局能量守恒（GEC）出发，构建各向异性多相多孔压电介质的线性动力学与本构理论：从抽象能量密度泛函出发，通过泰勒展开与对称性约束推导得到标准的动能密度、势能密度与电焓，而非先验假设它们；对GEC积分进行局域化处理，得到多相动量方程、高斯定律、耦合本构关系及边界条件作为数学推论，无需引入牛顿定律或哈密顿原理。该框架完全消除了虚拟质量参数，相间惯性耦合由非对角动能系数ρ_{ij}^{αβ}自然产生；由于所有系数均源自单一光滑势，施瓦茨定理自动保证麦克斯韦互易性与完全热力学自洽性。这些公式与哈密顿原理推导结果一致，且在各自极限下可精确退化为Biot多孔弹性理论与Tiersten单相压电理论。最后，线性平面波分析得到广义克里斯托费尔特征值方程，对水饱和多孔PZT-2的数值相速度计算展示了模态结构并揭示了强定向机电耦合特性。
英文摘要
Multiphase porous piezoelectric media are essential for advanced transducers and smart sensors. Existing theories typically postulate Newton's second law for each phase or rely on phenomenological Hamiltonian constructions. The former forces \emph{ad hoc} virtual-mass tensors to describe interphase inertia, while the latter provides no intrinsic safeguard against thermodynamic inconsistency when piezoelectric and multiphase couplings are superposed. In this work, we establish a linear dynamic and constitutive theory for anisotropic multiphase porous piezoelectric media from global energy conservation (GEC). From an abstract energy density functional, Taylor expansion and symmetry constraints derive the standard kinetic and potential energy densities and electric enthalpy, rather than assuming them a priori. Localization of the GEC integral yields the multiphase momentum equations, Gauss's law, the coupled constitutive relations, and the boundary conditions as mathematical corollaries, without invoking Newton's law or Hamilton's principle. The framework eliminates virtual-mass parameters entirely: interphase inertial coupling emerges organically from the off-diagonal kinetic-energy coefficients $ρ_{ij}^{αβ}$. Because all coefficients derive from a single smooth potential, Schwarz's theorem automatically guarantees Maxwell reciprocity and full thermodynamic self-consistency. The formulations agree with those from Hamilton's principle and reduce exactly to Biot's poroelastic theory and Tiersten's single-phase piezoelectric theory in the respective limits. Finally, linear plane-wave analysis produces a generalized Christoffel eigenvalue equation, and numerical phase-velocity calculations for water-saturated porous PZT-2 illustrate the modal structures and reveal strongly directional electromechanical coupling.
