Dynamic Analysis of Magnetoelasticity for Ferromagnetic Plates with Nonlinear Magnetization in Magnetic Fields

Based on a generalized variational principle of magnetoelasticity and Hamilton's principle, a dynamic theoretical model is developed for magnetoelastic vibration of a soft ferromagnetic plate with nonlinear magnetization being in a stationary magnetic field. The fundamental equations of the magnetic field and the motion of the ferromagnetic plate are derived together with the expression of equivalent magnetic force acting on the ferromagnetic plate as a result of the reciprocity between the magnetizable ferromagnetic plate and the applied field. There involve twofold nonlinearities in which one is from the magnetoelastic coupling and the other arises from the nonlinear magnetization of the ferromagnetic medium. A numerical technique that combines the finite-element method for magnetic-field distribution with the finite-difference and Newmark methods for vibration of the ferromagnetic plate is proposed. Analyses of the dynamic behaviors and stability characteristics of a ferromagnetic cantilevered beam-plate vibrating in an applied stationary magnetic field are implemented numerically, which show that the frequency of magnetoelastic vibration of the ferromagnetic beam-plate increases with the intensity and the incident angle of the applied magnetic field, and that the magnetization nonlinearity obviously influences the magnetoelastic dynamics behavior. Especially for strong magnetic fields and certain geometrical parameters of the ferromagnetic plate, the magnetoelastic dynamic behavior of the ferromagnetic plate, taking into account nonlinear magnetization, exhibits distinctive magnetoelastic characteristics compared with that of the ferromagnetic plate with linear magnetization. DOI: 10.1061/(ASCE)EM.1943-7889.0000518. (C) 2013 American Society of Civil Engineers.