DOI: https://doi.org/10.32347/2410-2547.2019.102.109-120

### Stress-strain state and equation of the vertical movement of the cored body of rotation – disc under electromagnetic fields

#### Abstract

Investigeted the problem of the theory of thermoelasticity and electromagnetoelasticity for solid of revolution, in particular a cored disk of variable thickness, loaded by an axisymmetric temperature field and volume forces: gravity forces, ponderomotive forces (mechanical forces acting per unit volume of the conducting medium) and inertia forces is considered.

The problem of determining the equilibrium or motion of a continuous bounded medium is a complex problem. For solving it is necessary to first solve the equations mechanics of continue together with the equations of electrodynamics into account the thermomechanical interaction of the environment as a result the deformation. While investigating the stress state of an electrically conductive body in an electromagnetic field, it is assumed that the body is in a magnetic field created by an electric current in the body itself, where an electric current flows and electric charges are generated. Under the influence of its own electromagnetic impulse field, the body must move independently. In circuits in which an alternating current flows in magnitude and constant in direction, Newton's law is not valid (the equilibrium condition of the ponderomotive forces the mechanical forces acting on the body from the side of the electromagnetic field). These forces will also cause the motion of the body of revolution.

As a result of the research, differential equations were obtained for the determination of displacements and the equation for the vertical motion of a body of revolution of variable thickness.

The conditions for the movement of the cored disk under the action of its own electromagnetic pulse field are determined. The stress state of the rotating body is investigated. It was shown that the tangential, axial and radial stresses in the body of the cored disk are absent, that is they are equal to zero. The only voltage other than zero is the circumferential tension. It is shown that the temperature field appears when the ponderomotive forces caused by the electromagnetic field arise and is the result of deformation of the body of rotation - a cored disc.

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Parton V., Pearlyi P. Metodyi matematicheskoy teorii uprugosti (Methods of the mathematical theory of elasticity). - M.: Nauka, 1981. - 428 p.

Sedov L. Mehanika sploshnoy sredy (Continuum Mechanics). - M.: Science, 1976. - Vol. I. - 483 p.

Germain P. Kurs mehaniki sploshnyh sred (Course in the mechanics of continuous media). - Moscow: Higher School, 1983. - 399 p.

Timoshenko S., Goudier J. Teoria uprugosti (Theory of Elasticity). - Moscow: Nauka, 1979. - 560 p.

Yavorsky B., Pinsky A. Osnovy fiziki (Basics of physics). - Moscow: Nauka, 1981.-1. -396 с.

Melan E., Parkus G. Temperaturnye napriazhenia, vyzyvaemye stacionarnymi potokami (Temperature stresses caused by stationary fields). - Moscow: Fizmatgiz, 1982. – 167 s.

Saveliev I. Kurs obschey fiziki (The course of general physics). - Moscow: Fizmatgiz, 1982. - Vol.1 -411s.

Timoshenko S. Kurs teorii uprugosti (Course of the theory of elasticity). - K .: Naukova Dumka, 1972. - 501s.

Ryabov A., Fedorenko Y. Ob odnom metode reshenia zadachi teorii uprugosti dlia tel vraschenia (A method for solving the elasticity problem for bodies of revolution, Mat. methods and physical-mechanical fields). - 1988. - Issue. 28. - p. 58 - 62.

Grevtsev A. Reshenie zadachi termouprugosti dlya vraschauschihsia aksial’nyh tel peremennoy tolschiny (Solution of the problem of thermoelasticity for rotating axial bodies of variable thickness). // Construction and architecture. Novosibirsk, 1991. - № 4. - p.33 - 37.

Grevtsev A. Pro odyn metod rozv’iazannia osesymetrychnoi zadachi teorii pruzhnosti dlia nerivnomirno nagritogo obertovogo dyska zminnoi tovschiny (About one method of solving an axisymmetric problem of elasticity theory for an unevenly heated rotating disk of variable thickness). // Resistance of materials and theory of structures. - 1998. - Vip. 64. - P. 76-86.

Grevtsev A., Kharchenko S. Pro odyn metod rozv’iazannia osesymetrychnoi temperaturnoi zadachi teorii termopruzhnosti dlia nerivnomirno nagrityh til obertannia (About one method for solving the temperature problem of the theory of thermoelasticity for unevenly heated bodies of rotation). // Resistance of materials and theory of constructions. - 2003. - V. 73. - P. 65-72.

Madelung E. Matematicheskiy apparat fiziki (Mathematical apparatus of physics). - Moscow: Fizmatgiz, 1961. - 292 p.

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