Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method

This study examined the dynamic characteristics of nonlinear electrostatic pull-in behavior for shaped actuators in micro-electro-mechanical systems (MEMS). The natural frequencies of a fixed-fixed shaped beam vibrating around its statically deflected position were calculated using the differential quadrature method (DQM). The proposed model included the nonlinear interaction between the curved electrostatic field force and the shaped micro-beam, as well as the mid-plane stretching, axial residual stress and electrical field fringing effect. Very good agreement existed between the results simulated using the proposed model and the measured data. This work also investigated the micro-beam and electrode shape effect on the natural frequencies of the actuator system. Analytical results indicate that the variation in the micro-beam and the electrode shapes might not only influence the electrostatic field distribution but also significantly alter the dynamic characteristics of the micro-actuator. Analytical results demonstrate that the shaped micro-beam with curved electrode can increase the working voltage range approximately six times compared to the rectangular micro-beam and flat electrode.