Natural Frequencies of Magnetoelastic Longitudinal Wave Propagation in an Orthotropic Circular Cylinder

Abstract

In this paper, we study the longitudinal wave propagation in a perfectly conducting elastic circular cylinder in the presence of an axial initial magnetic field. The elastic cylinder is assumed to be made of an orthotropic material. The problem is represented by the equations of elasticity taking into account of the effect of the magnetic field as given by Maxwell's equations in the quasi-static approximation.  The stress free conditions on the inner and outer surfaces of the hollow circular cylinder are used to form a frequency equation in terms of the wavelength, the cylinder radii and the material constants. Numerical calculations are obtained and the results are represented graphically. It is observed that the longitudinal elastic waves in a solid body propagating under the influence of a superimposed magnetic field can be different significantly from that of those propagating in the absence of a magnetic field. Also, elastic waves may convey information on electromagnetic properties of the material: for example through a precise measurement of the surface current induced by the presence of the magnetic field. Finally, some of the earlier results are deduced as particular cases.

Keywords: Natural frequencies, Magnetoelasticity, Longitudinal wave, Orthotropic materials,