Magnetoelastic Coupled Nonlinear Free Vibration of Rectangular Microplates

This paper studies the nonlinear free vibration behaviors of microplates in a magnetic field. The magnetizing force exerted on the microplate is obtained with magnetoelastic interaction theory. By the modified strain gradient theory (MSGT), the size hardening effect of the microplate model based on the Kirchhoff plate is characterized. Geometrical nonlinearityis considered to calculate kinetic and strain energy. Subsequently, the magnetoelastic coupled dynamics equilibrium equation is obtained via Hamilton’s principle. With the aid of Galerkin and multiscale methods, the discrete vibration equations and the nonlinear natural frequency of the microplate for different boundaries are obtained, respectively. Through numerical examples, the influences of length scale parameters, magnetic field strength, boundary conditions, initial values and geometric dimensional parameters on natural frequency are investigated. The results indicate that the reduction in structural dimensions and the increase in thickness or magnetic field strength cause an enhancement of stiffness, thereby elevating the natural frequency. Especially, as the initial value grows, natural frequency exhibits a complex trend of variation at different boundaries.