Vibration of a rotating flexible ferromagnetic disc subject to a solenoid electromagnet

A rotating flexible ferromagnetic annular disc with initial unstressed transverse runout subjected to a solenoid electromagnet is modelled and investigated. The total transverse deflection of the steady-state response of the rotating disc is analysed, and the condition of undamped resonance induced by the initial transverse runout and the stiffness of the electromagnetic force is evaluated. A quadratic eigenvalue problem is obtained and employed to study natural frequency and dynamic stability of the rotating disc. Analytical results show that the solenoid electromagnet can cause not only dynamic instability but also system resonance of the rotating disc if it has the initial transverse runout; the instability and resonance tend to occur at a lower rotational speed with the increase of the stiffness of the electromagnetic force.