A plane axisymmetrical coupled dynamic problem of thermomechanics for an electroconductive hollow cylinder under homogeneous non-stationary electromagnetic action is formulated. To construct its solution, the approximation of the determining functions the axial component of the magnetic field strength vector, the temperature, and the radial component of the displacement vector with respect to the radial variable by cubic polynomials is used. As the result, the initial-boundary problem for determining functions is reduced to a Cauchy problem with respect to the time variable for the integral characteristics of these functions. The expressions of integral characteristics are obtained in the form of a convolution of functions describing the uniform solutions and the given limit values of determining functions. As an example, the amplitude-frequency characteristics of the radial stresses in the given cylinder are analyzed numerically, with taking into account the connectivity between the temperature and the displacement fields as well as without such accounting.

Using the approximation of the distributions of the axial component of the magnetic field stress vector, of temperature and radial displacements in the radial variable by cubic polynomials, we obtain a general solution of the connected dynamic problem of thermomechanics for an electric conductive hollow cylinder under the action of impulsed electromagnetic fields with amplitude modulation of characteristic types in modes with the impulsed modular signal, the damped sinusoid and the single electromagnetic impulse equal to the modular signal.

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