Static and Dynamic Analysis of Electrostatically Actuated MEMS Shallow Arches for Various Air-Gap Configurations

In this research, we investigate the structural behavior, including the snap-through and pull-in instabilities, of in-plane microelectromechanical COSINE-shaped and electrically actuated clamped-clamped micro-beams resonators. The work examines various electrostatic actuation patterns including uniform and non-uniform parallel-plates airgap arrangements, which offer options to actuate the arches in the opposite and same direction of their curvature. The nonlinear equation of motion of a shallow arch is discretized into a reduced-order model based on the Galerkin's expansion method, which is then numerically solved. Static responses are examined for various DC electrostatic loads starting from small values to large values near pull-in and snap-through instability ranges, if any. The eigenvalue problem of the micro-beam is solved revealing the variations of the first four natural frequencies as varying the DC load. Various simulations are carried out for several case studies of shallow arches of various geometrical parameters and airgap arrangements, which demonstrate rich and diverse static and dynamic behaviors. Results show few cases with multi-states and hysteresis behaviors where some with only the pull-in instability and others with both snap-through buckling and pull-in instabilities. It is found that the micro-arches behaviors are very sensitive to the electrode's configuration. The studied configurations reveal different possibilities to control the pull-in and snap-through instabilities, which can be used for improving arches static stroke range as actuators and for realizing wide-range tunable micro-resonators.