Destabilizing Effect of Magnetic Damping in Plate Strip

Abstract

Motion of an electrically conducting structural member in a magnetic field induces an electric current, which interacts with the magnetic field so as to inhibit the motion. This magnetic damping is known to have a destabilizing effect when the structure is subjected to an in‐plane longitudinal force. The dynamic stability of a plate strip in a magnetic field parallel to the plane of motion is considered with a special reference to the destabilizing effect due to the magnetic damping. The differential equation for the motion of the plate strip is first derived, and the free vibration of the system is studied. An explicit expression for the destabilizing effect is obtained. It is shown that the plate can become unstable without the in‐plane force at a critical field. Then the parametric excitation of the system due to the harmonic longitudinal force is considered. The governing equation is reduced to a well‐known Mathieu's equation; and dynamic stability of the system for various loading conditions is discussed.