A three dimensional solution for a magneto-elastic vibration in a sphere

A three dimensional solution for a magneto-elastic vibration in a sphere is considered. The normal mode method has been applied to free vibrations, and the Airy stress-function's approach gives solutions for the differential equations of motion. The response of the system due to forced vibrations is obtained by developing the external forces into linear combinations of all the normal modal functions. Numerical solutions for radial and transverse displacements have thus been obtained. Furthermore, graphical solutions for axisymmetric displacement have also been provided for different modes of free vibration. In the above-suggested analysis, the coupling of electromagnetic and elastic waves is considered from the standpoint of linear elasticity and linearized electro-magnetic theory. The investigation of this coupling effect predictably shows that the effect of the magnetic field is to lower the amplitude of the elastic vibration.