A Numerical Improvement in Analyzing the Dynamic Characteristics of an Electrostatically Actuated Micro-beam in Fluid Loading with Free Boundary Approach

In this paper, the dynamic response of a micro-beam immersed in a fluid with regard to the free boundary of the operating fluid is investigated. In the other words, in addition to the kinematic compatibility on the boundary between micro-beam and its surrounding fluid, equations of the potential functions are modeled considering the free boundaries. It is also assumed that the micro-beam is a movable electrode, and the electrostatic force is used for the actuation of the system. Galerkin’s method is utilized to solve the governing equations of the fluid-structure system. By imposing a fixed voltage to the system, in addition to investigating the geometrical effects, fluid type and the dimensions of the cavity, the effect of the free boundaries on the transient response of the system is studied. It is shown that the coefficient of relative permittivity of operating fluid, the length of the micro-beam, and the relative position of it to the lower side of the cavity have significant impact on the instability of system voltage. It is further shown that assuming the free boundaries in the modeling of the system, which is closer to the physical reality of the issue, increases the pull-in voltage.