Thermoelastic state of a magnetically soft layer in a magnetic field harmonic as a function of time with biasing
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THERMOELASTIC STATE OF A MAGNETICALLY SOFT LAYER IN A MAGNETIC FIELD HARMONIC AS A FUNCTION OF TIME WITH BIASING M. T. Solodyak
UDC 539.3: 538.54
We propose a procedure of approximate evaluation of the parameters of magnetic, temperature, and mechanical fields in a layer of magnetically soft material subjected to the action of an electromagnetic field specified by the values of the constant and periodic (as a function of time) components of the magnetic-field intensity on the surface. The procedure is based on the use of a small parameter defined as the ratio of the amplitude of the harmonic field to the constant component. We deduce the criteria of applicability of the proposed procedure according to which temperature should not exceed the Curie temperature and stresses should not exceed the elasticity limit.
Numerous contemporary technological procedures are based on the application of thermal treatment of conducting bodies by variable (as functions of time) electromagnetic fields. The electric currents induced in these bodies are accompanied by heat release and the action of ponderomotive forces. The values of the corresponding temperature fields and stresses can be quite high and exceed the acceptable levels. To estimate the characteristics of these fields, it is necessary to have efficient computational models aimed at finding the electromagnetic fields, heat release, temperature, and stresses depending on the external electromagnetic fields, the conditions of heat exchange of the body with the environment, mechanical conditions, electric, thermal, and mechanical characteristics of the material, etc. The thermoelastic state of conducting nonferromagnetic bodies in external harmonic (as functions of time) electromagnetic fields is studied in [1]. The case of conducting ferromagnetic (magnetically soft and hard) materials is investigated in [2–8]. Note that the analysis of the thermomechanical behavior of conducting bodies under the simultaneous action of two components of the external magnetic field (periodic and time-independent) is of high practical significance. In the present work, we consider the case of a magnetically soft layer. The procedure of numerical solution of the corresponding problem of magnetothermomechanics is theoretically justified in [9]. The required solution of the problem is constructed in three stages. In the first stage, by using the expansion of the equations of electrodynamics in a small parameter, we determine the magnetic field in the stationary approximation. After this, we write the corresponding expressions for the intensity of heat release and the density of energy of the magnetic field averaged over the period of oscillations of the external magnetic field. In the second stage, the temperature field is found from the heat-conduction equation in which the role of heat sources is played by the heat release determined in the first stage. In the third stage, the displacements and stresses are obtained from the equations of quasistatic thermoelasticity. In the equations of therm
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