Mathematical modeling in thermomechanics of electroconductive bodies under the action of the pulsed electromagnetic fields with modulation of amplitude

Abstract

A mathematical model of description and a method for determining the thermostressed state of non-ferromagnetic electroconductive bodies under the influence of external unsteady electromagnetic fields of pulsed type are proposed. Such fields have the character of a regime with amplitude modulation under the action of pulse modulated signal and are widely used in technologies of magnetic pulsed processing electroconductive materials. This model is the development of well-known models for quasi-steady and pulsed electromagnetic fields. As an example, the results of investigation of the thermomechanical behavior of solid and hollow cylinders under the influence of electromagnetic pulse are given.

Thermomechanical behavior of an electrically conductive cylindrical implant under the action of external unstable electromagnetic fields

“…The action of an external unstable EMF is given by the value of the axial component H z of the vector H on the surface r = R of the cylinder as a function [8…”

“…Time of action of unstable EMF is t i = t incr +t decr . Unsteady EMF, which is mathematically described by expression (24), has the character of impulsed EMF with amplitude modulation [8,9,[12][13][14][15][16][17]. Substituting the expression (24) of the function H + z (t) in the relation ( 3)-( 23), we obtain the expressions of Joule heat Q, radial component F r of the vector of ponderomotive force F and temperature T , radial displacements u r and corresponding stresses σ jj (j = r, ϕ, z) under the action of unstable EMF.…”

“…In this paper, a physical and mathematical model for determining the thermally stressed state of an electrically conductive cylindrical implant under the action of external unstable EMFs of characteristic types is proposed [8]. This model allows to predict the determination of the maximum allowable values of temperature and stress intensity according to physiological norms depending on the parameters of external unstable EMF [9] and the time of their action.…”

Solution of the connected problem of thermomechanics for a long hollow electroconductive cylinder under the action of impulsed electromagnetic field with amplitude modulation

“…An impulse EMF with amplitude modulation is given on the inner r = r 0 and outer r = r 1 surfaces of the cylinder considered by the values H ± z (t) of the tangential axial component H z (r, t), which are described by the dependence [5] H z ± (t) = H 0 ϕ 0 (t) sin(ωt + ϕ),…”

“…An important place among IEMF is occupied by IEMF with amplitude modulation. Some works [4][5][6] on the determination of the thermo-stressed state of conductive bodies of a canonical form under the action of stationary EMF and IEMF with amplitude modulation in the formulation of an unconnected problem of thermomechanics for such bodies are known from the literature. However, the influence of the process of thermoelastic energy dissipation under the action of IEMF with amplitude modulation on the thermo-elastic state of the electro-conductive cylinder is insufficiently studied.…”