Solution of plane dynamic boundary-value problems of electromagnetothermoelasticity for cylindrical bodies

We give the mathematical statement of a two-dimensional dynamic problem of electromagnetothermoelasticity for cylindrical bodies and deduce the primary equations of electrodynamics and thermoelasticity for the complex problem. The primary equations of the two-dimensional dynamic problem of thermoelasticity in stresses are reduced to a system of hierarchically connected wave equations. The boundary-value problems are formulated for a long hollow cylinder and a cylindrical beam whose cross section has the shape of a circular sector. These bodies are in the state of plane deformation and subjected to the action of a nonstationary electromagnetic field on their outer surfaces. We propose a method for the solution of these boundary-value problems.