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In this paper we study the propagation of longitudinal magnetoelastic waves in a rod
with damage. It is shown that for a stationary magnetic field the system of equations of
magnetoelasticity can be reduced to one evolution equation with respect to the function of
longitudinal deformation. The equation comprises variants of generalized unperturbed Burgers
equations, when the medium does not have conductivity. For these equations, solutions have
been found in the form of stationary shock waves. The connection between the main parameters
(amplitude, width of the front) of the shock wave and the parameters of the system have been
established. The influence of the damage parameters and the elastic nonlinearity of the material
on the width of the front of the shock wave is determined. The evolutionary equation of
magnetoelasticity has been investigated by an approximate method, when the medium is
conductive. The influence of the conductivity parameters of the medium and material damage
on the amplitudes of the first and second harmonics of the decomposition has been analyzed.
Keywords: longitudinal deformation; nonlinearly elastic rod; material damage; magnetic field; evolutionary equation; asymptotic solution. |
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