Nonlinear natural vibration of a circular plate in the non-uniform induced magnetic field

The magnetoelastic nonlinear natural vibration of the conductive thin circular plate in non-uniform induced magnetic field in the current-carrying circular coil is presented. Based on electromagnetic theory, elliptic integral expression of magnetic field and electromagnetic force is deduced. The magnetoelastic vibration equation of plate is derived through the Hamilton principle. Then through Galerkin method, nonlinear vibration differential equation is developed. By the multiple-scale method, the natural frequency expression is achieved. Through numerical calculation, the magnetoelastic vibration characteristics diagrams are drawn. The influences of coil current, plate geometric parameters and time on natural frequency, electromagnetic torque and singular point are discussed. The results show that natural frequency increases when plate thickness becomes larger, but decreases as current or plate radius increases. Along radial direction, magnetic field increases nonlinearly and electromagnetic torque manifests different variations under different boundary conditions. Additionally, when the current is off and on, equilibrium point is center and stable focus, respectively. The obtained results are validated by comparing with the previously reported work and those from numerical method.