Abstract
The radial vibrations of a thick transversely isotropic elastic cylinder subjected to a uniform axial magnetic field are considered. The problem is described by the equations of elasticity taking into account the effect of the magnetic field and the electro-magnetic equations of Maxwell. This requires the solution of the equations of motion in cylindrical coordinates with thez-axis directed along the axis of the cylinder. The frequency equations have been derived in the form of a determinant involving Bessel functions. The roots of the frequency equation give the values of the characteristic circular frequency parameters of the first four modes for various geometries. These roots, which correspond to various modes, are numerically calculated and presented graphically. This study shows that waves in a solid body propagating under the influence of a superimposed magnetic field can differ significantly from those propagating in the absence of a magnetic field. Also, the circular frequency increases with decreasing wall thickness of the cylindrical shell for all modes and increase with the higher modes of motion. Finally, it is noticed that the effect of the magnetic field on the mode frequency becomes less significant for the higher modes.
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Abd-alla, Aen.N. Magneto-elastic radial vibrations of a transversely isotropic hollow cylinder. Japan J. Indust. Appl. Math. 14, 469–482 (1997). https://doi.org/10.1007/BF03167393
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DOI: https://doi.org/10.1007/BF03167393