Effects of an in-plane axisymmetric magnetic field on the vibration of a thin conductive spinning disk

This paper details the derivation and solution of the governing equation for linear transverse vibrations of a thin perfectly conducting rotating disk subjected to an axisymmetric in-plane magnetic field having a circumferential flux pattern. Previous works on plates and shells have hypothesized that the application of a magnetic field is capable of increasing the natural frequency of a thin conductive plate. Analytical results show a significant increase in maximum stable operating speed of a thin disk in the presence of a magnetic field. The effect is dependent on both thickness and magnetic field strength.