Influence of material damage on propagation of a longitudinal magnetoelastic wave in a rod

At present, continuum damage mechanics is in good progress, studying both the stress-strain state of structures and the accumulation of damages in their materials. Treatment of a number of problems is associated with the necessity of taking into account the fact that structural elements operate under the action of external magnetic field, which affects the formation and propagation of elastic waves. In this work, for an electrically conducting rod performing longitudinal oscillations, we formulate a self-consistent system, which includes the equation of rod dynamics, the equation of variation of the external magnetic field strength, and the kinetic equation of accumulation of damage in the material of the rod. Here we assume that damage is uniformly distributed in the rod material, the magnetic field is stationary and use the classical model of the homogeneous Bernoulli rod as the rod model. The linearized system and the system of equations, including geometrical and physical elastic nonlinearities, are considered sequentially...