On the Investigation of One-Dimensional Models of Thermo-Electro-Magneto-Elastic Bars

摘要

In this paper a linear dynamic model of thermo-electro-magneto-elastic bars made of anisotropic inhomogeneous material is considered. An algorithm of approximation of the corresponding three-dimensional initial-boundary value problem by one-dimensional problems for bar with variable cross-section is constructed, when density of surface force, and components of the electric displacement and magnetic induction along the outward normal vector of the boundary are given on the lateral face surfaces of the bar. The obtained one-dimensional initial-boundary value problems are investigated in suitable function spaces. Moreover, it is proved that the sequence of vector-functions of three space variables, restored from the solutions of the constructed one-dimensional problems, converges, in the corresponding function space, to the exact solution of the original three-dimensional initial-boundary value problem and, under additional conditions, the rate of convergence is estimated.