 Authors, 2014  Radiotekhnika, 2014 S. A. Lurye - Dr.Sc. (Eng.), Professor, Head of Laboratory, Institute of Applied Mechanics, Russian Academy of Sciences (RAS IPRIM) (Moscow). E-mail: lurie@ccas.ru P.A. Belov- Ph.D. (Phys.-Math.), Researcher, Research and Education Center «New materials, composites and nanotechnology», (IC). E-mail: BelovP@yandex.ru L.N. Rabinskiy - Dr.Sc. (Phys.-Math.), Professor, Dean of the number 9, Moscow Aviation Institute (National Research University) O.V. Egorova - Ph.D. (Phys.-Math.), Associate Professor, Moscow Aviation Institute (National Research University)

We develope the variational model of the couple thermoelasticity and electrodynamics. Model couple dynamic thermoelasticity is constructed as a four-dimensional variant of the theory of elasticity of the medium, transversely isotropic with respect to the time coordinate. Variational formulation allows us to establish constitutive equations, «equilibrium» equations of the continuum and the corresponding spectrum of the boundary conditions. Generalized equilibrium equations describe the motion of a three-dimensional medium, heat equation, which takes into account the wave properties of heat distribution. As a result, given the closed and correct variational formulation of extended thermodynamics theory. Similarly, a model of electrodynamics is elaborated. In this case the normalized four-vector potential of the electromagnetic field play the role of displacements. Faraday equation are treated as compatibility equations, Ampere equations are interpreted as the equilibrium equations. This variational «unification» of the models of electrodynamics and continuum mechanics, gives the opportunity to build a dynamic model of couple thermo-electric magnetoelasticity for spatially isotropic media. Couple model of thermo-electromagnetoelasticity built as a model of conditional connected medium consisting from two embedded into each other and interacting with each other environments: first media is the dynamic thermoelasticity, second media is the electromagnetic media (electromagnetic field). Proposed variant of non-classical electrodynamics allows interaction with spatially isotropic material through the «temperature» and «pressure» by means of linear combinations of magnetic and electric potentials, as well as through the analog deviatoric shear stresses. It was found that the generalized model of couple thermo-electromagnetoelasticity is formulated, This model allows an extended range of physical interactions with deformable media. All of the classical equations of electrodynamics are satisfied. Analysis of the defining relations predicts new dynamic, thermal, electrical and magnetostrictive effects for isotropic media. Variational approach allows to get the generalized couple gradient theory of thermo- electromagnetoelasticity.

 

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