Determination and optimization of the thermally stressed state of electrically conducting bodies in external quasistationary electromagnetic fields

Gachkevich, A. R.

doi:10.1007/bf01095871

Cited by 3 publications

(10 citation statements)

References 2 publications

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“…Then the problem (9), (10), (7) can be written as follows for a closed shell (25), we write the respective systems of equations and boundary conditions for the characteristics of a quasistatic electromagnetic fields in plates [1,2].…”

Section: L~; -Aj O%-7 + (K~ + K)b + A-7 O~--t'mentioning

confidence: 99%

“…= j(t)Re{j(r)ei~t}, electric field intensities E. = j(t)Re {E(r)ei~t}, E (~ = j(t)Re {E(~ and magnetic field intensities H. = j(~)Re {H(r)e~t}, H(. ~ = j(t)Re//(~ in the region D of the body and Do of the surrounding medium, taking account of relations (1) and (2) (see [1]):…”

mentioning

confidence: 99%

“…The subscripts ~-and n denote the tangential and normal components of the respective vectors on the surface S. Equations (3) can be reduced by a known method [1,5] to a system of equivalent equations in the functio,s E, E (~ or H, H (~ Such a system in E and E(o) has the form…”

mentioning

confidence: 99%

“…We recall that finding these parameters is the first step in computing the thermoelastic state of electrically conducting shells perturbed by an electromagnetic field [1].…”

mentioning

confidence: 99%

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On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

Gachkevich¹,

Chornii²

1996

J Math Sci

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We state the initial equations and the boundary conditions for determining the parameters that describe a quasistatic electromagnetic field perturbed by the action of external electric currents in a thin nonferromagnetic shell.Consider a thin electrically conducting shell of constant thickness 2h in a region D in which there is no charge or current. The shell is situated in a dielectric medium Do (which we assume to be approximately a vacuum) and subject to the action of a quasistatic electromagnetic field. The field is generated by a system of quasistatic currents flowing in Do (an inductor of time-varying intensity), given by the expressionwhere r is the radius-vector of the point, w is the cyclic frequency, t is time, r is the initial phase, and jA(r, t) j(t)j~r) is the amplitude, which varies only slightly over the period of an electromagnetic wave, f. = 2pi/w, so that the following condition holds:We pose the problem of determining the parameters that describe the electromagnetic field under such an action in the shell-external medium system. We recall that finding these parameters is the first step in computing the thermoelastic state of electrically conducting shells perturbed by an electromagnetic field [1].We shall start from Maxwell's equations for the external medium (a vacuum) and a solid isotropic nonferromagnetic nonpolarized motionless body with constant (averaged over a temperature interval) material characteristics and neglecting the displacement currents [5]. We write the following system of independent equations with complex current density j. = j(t)Re{j(r)ei~t}, electric field intensities E. = j(t)Re {E(r)ei~t}, E (~ = j(t)Re {E(~ and magnetic field intensities H. = j(~)Re {H(r)e~t}, H(. ~ = j(t)Re//(~ in the region D of the body and Do of the surrounding medium, taking account of relations (1) and (2) Here jg~ = f(r)e ~o is the complex amplitude of the given current density in the surrounding medium; E, H, E (~ and H (~ are the complex amplitudes of the intensities of the electric and magnetic fields in the regions D and D O respectively; ~ = eo~., and # = #0#.~o, and #o are the dielectric permittivity and magnetic permeability of the body and the magnetic permeability of the vacuum; a is the electrical conductivity of the body.Equations (3) must be supplemented by the independent coupling conditions of the characteristics of the electromagnetic field at the interface between the body and the surrounding medium:

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Section: L~; -Aj O%-7 + (K~ + K)b + A-7 O~--t'mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…We recall that finding these parameters is the first step in computing the thermoelastic state of electrically conducting shells perturbed by an electromagnetic field [1].…”

mentioning

confidence: 99%

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On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

Gachkevich¹,

Chornii²

1996

J Math Sci

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“…Ya. Burak [11,16,19]. In these models, it is assumed that, with respect to a body, an EMF is an external action, whose influence on heat conduction and deformation processes are taken into account in thermoelasticity equations through the factors of action, namely volume heat sources (heat release, specifically the Joule heat and heat released as a result of depolarization and demagnetization) and volume (ponderomotive) forces of the action of an EMF on charges and currents, including polarization ones.…”

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confidence: 99%

Some problems of mathematical modeling in thermomechanics of bodies of various transparencies subjected to thermal irradiation

2010

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Features of the statement of problems of thermomechanics for solids of various transparencies for thermal radiation are presented. Approximate approaches to the calculation of temperature in semitransparent solids are analyzed. We investigate the influence of the effects of radiation and transfer of thermal energy on temperatures and stresses in semitransparent and opaque solids on a model problem for an irradiated layer.

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Mathematical models of thermomechanics of magnetizable and polarizable electrically conducting bodies subject to quasisteady electromagnetic radiation

Hachkevych¹

1999

J Math Sci

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We give a brief survey of recent research on the problems of mathematical modeling of the thermomechanical behavior of deformable bodies with different electrical conductivity, magnetizability, and polarizability subject to a quasisteady electromagnetic field in the radio and infrared frequency ranges.The joint study of mechanical, thermal, and electromagnetic processes in electrically conducting bodies has attracted the attention of researchers because of the wide practical application of electromagnetic fields over the past few decades in the manufacture and processing of structural elements and devices made of traditional and new electromagnetic materials [54,55]. To construct rational regimes for such processes or use of equipment that functions subject to electromagnetic loads, it is necessary to create a method of mathematical modeling and effective methods of determining the thermostressed state of bodies of arbitrarily electrical conductivity that are magnetizable and polarizable and subject to external electromagnetic fields, in particular the quasistatic fields [36,40] that are widely applied in engineering practice.The system of initial equations of the physico-mathematical model for determining the thermostressed state of electrically conducting bodies subject to an electromagnetic field taking account of the interaction of mechanical, thermal, and electromagnetic processes includes the equations of electrodynamics and thermomechanics with heat sources and bulk force factors (ponderomotor forces and moments) caused by the electromagnetic field. Such a system is coupled and nonlinear, when account is taken of the generalized Ohm's law, the relations between the inductions and intensities of the electric and magnetic fields for arbitrarily moving conducting media that can be magnetized and polarized [36,42], the expressions for the force factors and heat emission [34,42], the coupling of the strain and temperature fields [33], and the temperature dependence of the characteristics of the material [10,33].Since rigid bodies may differ significantly in electrophysical properties and the general theory of interaction of an electromagnetic field with a material continuum mentioned above is rather complicated, it is vital to construct specially designed variants of the theory of interaction for smaller classes of materials by taking account of the specifics of their characteristic properties in processes involving electrical conduction, magnetization and polarization as functions of the amplitude-frequency characteristics of the electromagnetic field [ 10,34].In a number of studies in determining the thermostressed state of electrically conducting nonferromagnetic unpolarized bodies in a quasistatic and nonstationary (in particular, pulsing) electromagnetic field, the effect of this field on the processes of heat conduction and strain is taken into account through the Joule heat emission and the ponderomotor forces, while the effect of motion of the medium on the current is assumed unimportant [40,55].In this...

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Determination and optimization of the thermally stressed state of electrically conducting bodies in external quasistationary electromagnetic fields

Cited by 3 publications

References 2 publications

On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

Some problems of mathematical modeling in thermomechanics of bodies of various transparencies subjected to thermal irradiation

Mathematical models of thermomechanics of magnetizable and polarizable electrically conducting bodies subject to quasisteady electromagnetic radiation

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