Nonlinear dynamics of elastic ferromagnetic microplates subjected to motion effect

In this paper, based on the modified strain gradient theory and Kirchhoff thin plate theory, a nonlinear magnetoelastic coupling size-dependent dynamics model is developed for ferromagnetic microplates with axial motion in magnetic field. The model can capture size effect and evaluate electromagnetic, magnetization, and motion effects, as well as reveal the coupling mechanisms of the interaction and superposition of multiple effects. The nonlinearity in the model includes not only von-K ' arm ' an geometric nonlinearity, but also nonlinear magnetization caused by magnetic saturation and hysteresis phenomena of ferromagnetic materials. Based on the modified strain gradient theory (MSGT) to introduce three strain gradients for capturing size effect, and considering eddy effect, nonlinear magnetization and deformation perturbed magnetic field, the nonlinear magnetoelastic size-dependent governing equations of motion for axially moving ferromagnetic microplates are derived using the Hamilton's principle. According to the proposed theoretical model, the Galerkin and KBM methods are used to obtain the frequency response equations under first- and second-order approximations for the primary resonance of simply supported microplates. The applicable parameter range is determined for the first-order frequency response equation, and the static bifurcation analysis is performed. The effect of geometric parameters, length-scale parameters, magnetic induction intensity, harmonic excitation load, and axial velocity on size-dependent dynamics behavior of systems is shown through the visualization of frequency response equations. The results show that the motion effect and size effect characterized by strain gradients weaken and enhance the system stiffness, respectively. The increase in plate thickness leads to the weakening of size effect but enhances the electromagnetic damping generated by Lorentz force, which causes the hardening behavior of system to increase but the resonance amplitude to decrease. The magnetic field suppresses the vibration of microplates to improve structural stability. Since it is the first analysis of ferromagnetic microplates in magnetic field, the results can serve as benchmarks for further analysis.