Dynamic pull-in and oscillations of current-carrying filaments in magnetic micro-electro-mechanical system

The initial value problem used for modeling a magnetic actuator arising from the design of a magnetic Micro-Electro-Mechanical Structure (magMEMS) with current-carrying filaments is derived using the concept of mutual inductance. The resulting model differential equation is nonlinear since it contains a term corresponding to the magnetic force between two filaments of finite length. The dynamic pull-in which occurs in the magMEMS model with one fixed and one moving filament is analyzed. The closed form approximate conditions for the dynamic pull-in are established in terms of model parameters. Approximate periodic solutions are derived analytically and numerical simulations are used for verification. These results are useful for understanding the modeling and operation of single-degree-of-freedom magMEMS.