Magnetoelastic oscillation of current-carrying plates in an alternating magnetic field

Modern technological advancements, particularly in micro- and nanoelectronics, aerospace engineering, sensor systems, and robotics, necessitate a deeper understanding of how structural elements behave under various physical influences. One significant and relevant phenomenon is magnetoelastic interaction, which involves how the mechanical behavior of current-carrying elastic bodies is affected not only by external loads but also by internal electromagnetic processes. Current-carrying plates, commonly utilized in micro- and nanoelectronics, respond to external fields by altering their stress-strain states. To accurately model these processes, an integrated approach is required that considers mechanical, electromagnetic, and thermal effects caused by electrical currents. This paper focuses on the mathematical modeling and numerical study of transverse magnetoelastic oscillations in thin current-carrying plates subjected to an alternating magnetic field. The problem is formulated considering electromagnetic interactions, geometric nonlinearity, and external alternating currents. A comprehensive system of equations is developed that includes the equations of motion, Maxwell's equations, and the heat equation with Joule heating sources. For the numerical solution, the finite difference method using the Newmark scheme and discrete orthogonalization techniques are applied. Graphs illustrating stress and strain distributions are presented, and the effects of magnetic field frequency and external current on the system’s behavior are analyzed. This research is vital for designing reliable components in micro- and nano-electronics and aviation.