Axisymmetric Nonlinear Free Vibration of a Conductive Annular Plate Under Toroidal Magnetic Field

The magnetoelastic nonlinear free vibration of a conductive thin annular plate in non-uniform magnetic field generated by the long straight current-carrying wire is presented. Based on electromagnetic theory, expressions of the non-uniform magnetic field and electromagnetic force are derived. According to the Hamilton principle, magnetoelastic nonlinear vibration equation of plate is derived. The Galerkin integral method is used to derive axisymmetric vibration differential equation. By method of multiple scales, natural frequency is then obtained. In numerical calculation, the nonlinear natural vibration characteristic curves show influence of different control parameters, e.g., current intensity, and plate size on natural frequency and electromagnetic force. Results show that natural frequency decreases first and then stabilizes with current, increases significantly with plate internal radius and thickness. The plate under boundary condition of internal radius simply supported and outer radius clamped exhibits hard characteristics. Magnetic induction intensity and electromagnetic force shows different changing rules along radial direction.