Computer analysis of the thermoelastic behavior of a steel rod with a thin copper coating during pulse electromagnetic action

A physical-mathematical model for determination of the thermostressed state of a steel rod with a thin copper coating is proposed. The criteria for evaluating its performance based on the parameters of an external, non-stationary electromagnetic influence are established. Initial-boundary value problems for the considered rod are formulated to obtain the determining functions, including the axial component of the magnetic field intensity vector, temperature, and radial displacement vector. A technique for constructing solutions of these initial-boundary value problems is proposed, utilizing approximation of the distributions of the determining functions within the rod and coating by quadratic polynomials in the radial variable. Consequently, the original problems related to determining functions are transformed into corresponding time-dependent Cauchy problems involving integral characteristics of these functions with respect to the radial variable. The general solutions of the Cauchy problems under the consistent influence of a non-stationary electromagnetic field are determined. Based on the performed computer analysis, the regularities of changes in ponderomotive force, temperature, radial and circular stresses in the considered rod were analyzed under the impact of an electromagnetic pulse.