Coupled Non-stationary Longitudinal Vibrations of an Infinite Electromagnetoelastic Rod

We study the associated non-stationary longitudinal vibrations of an infinite electromagnetoelastic rod. It is assumed that the material of the rod is a homogeneous isotropic conductor. In this case, the initial electromagnetic field, the Lorentz force, Maxwell’s equations and the generalized Ohm’s law are taken into account. Assuming that the desired functions depend only on the longitudinal coordinate, using the corresponding relations for the shells, a closed system of equations of motion is obtained. The desired functions are assumed to be bounded, and the initial conditions to be zero. The Fourier transform in the coordinate and the Laplace transform in time, as well as the small parameter method characterizing the relationship of mechanical and electromagnetic fields, are used to solve this problem. The solution is presented in integral form with the cores in the form of Green functions for which images and originals are constructed. An example of calculation is given.