A physical and mathematical model for determining the thermostressed state of an electroconductive solid ball under the action of an amplitude modulated radioimpulse is proposed. The centrally symmetric problem of thermomechanics for the considered ball is formulated. The azimuthal component of the magnetic field strength vector, temperature, and the radial component of the displacement vector were chosen as the determining functions. To construct solutions of the formulated components of the initial-boundary value problems of electrodynamics, heat conductivity, and thermoelasticity, a polynomial approximation of the determining functions over the radial variable is used. As a result, the initial-boundary value problems on the determining functions are reduced to the corresponding Cauchy problems on the integral characteristics of these functions over the radial variable. General solutions of Cauchy problems under homogeneous nonstationary electromagnetic action are obtained. Based on these solutions, the change in time of Joule heat, ponderomotor force, temperature and stresses in the ball under the action of amplitude-modulated radioimpulse depending on its amplitude-frequency characteristics and duration is numerically analyzed.

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