arXiv subjects

Xiuming Wang

Publications and source records attributed to Xiuming Wang.

4 recordsLinked to original sources

arXiv2026

Formulations of elastodynamic equations for anisotropic multiphase porous piezoelectric media based on global energy conservation

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 $\rho_{ij}^{\alpha\beta}$. 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.

physics.gen-ph↗

arXiv2022

Formulations of the Elastodynamic Equations in Anisotropic and Multiphasic Porous Media from the Principle of Energy Conservation

Elastodynamic equations have been formulated with either Newton's second law of motion, Lagrange's equation, or Hamilton's principle for over 150 years. In this work, contrary to classical continuum mechanics, a novel strategic methodology is proposed for formulating general mechanical equations using the principle of energy conservation. Firstly, based on Hamilton's principle, Hamilton's equations, Lagrange's equation, and the elastodynamic equation of motion are derived in arbitrarily anisotropic and multiphasic porous elastic media, for the first time. Secondly, these equations are all formulated using the principle of energy conservation for the related media. Both formulation results using the two kinds of principles are compared and validated by each other. The advantages of our methodology lie in that, the elastodynamic equation of motion, Lagrange's equation, and Hamilton's equations in continuum mechanics are directly formulated using a simple constraint of energy conservation without introducing variational concepts. It is easy to understand and has clear physical meanings. Our methodology unlocks the physics essences of Hamilton's principle in continuum mechanics, which is a consequence of the principle of energy conservation. Although the linear stress-strain constitutive relation is considered, our methodology can still be used in a nonlinear dynamical system. The methodology also paves an alternative way of treating other complex continuous dynamical systems in a broad sense. In addition, as an application, the continuity conditions at various medium interfaces are also revisited and extended using our proposed approach, which explains the law of reflections and refractions.

physics.class-ph↗

arXiv2021

A methodology for formulating dynamical equations in analytical mechanics based on the principle of energy conservation

In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and Hamilton-Jacobi's equation are all formulated based on the principle of energy conservation with a simple energy conservation equation, i.e., the rate of kinetic and potential energy with time is equal to the rate of work with time done by external forces; while D'Alembert's principle is a special case of the law of the conservation of energy, with either the virtual displacements ('frozen' time) or the virtual displacement ('frozen' generalized coordinates). It is argued that all of the formulations for characterizing the dynamical behaviors of a system can be derived from the principle of energy conservation, and the principle of energy conservation is an underlying guide for constructing mechanics in a broad sense. The proposed methodology provides an efficient way to tackle the dynamical problems in general mechanics, including dissipation continuum systems, especially for those with multi-physical field interactions and couplings. It is pointed out that, on the contrary to the classical analytical mechanics, especially to existing Hamiltonian mechanics, the physics essences of Hamilton's variational principle, Lagrange's equation, and the Newtonian second law of motion, including their derivatives such as momentum and angular momentum conservations, are the consequences of the law of conservation of energy. In addition, our proposed methodology is easier to understand with clear physical meanings and can be used for explaining the existing mechanical principles or theorems. Finally, as an application example, the methodology is applied in fluid mechanics to derive Cauchy's first law of motion.

physics.class-ph↗

arXiv2021

Dynamic Equation in Thermo-piezoelectric Dissipative Media from Energy Conservation

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.

physics.app-ph↗