Static and dynamic actuations of clamped-clamped V-shaped micro-resonators under electrostatic forces

This work presents detailed static and dynamic analysis of electrostatically actuated in-plane micro-electro-mechanical V-shaped micro-beam resonators. An analytical model is presented, based on the Euler Bernoulli beam theory, which accounts for the nonlinear electrostatic forces and the mid-plane stretching. The model is utilized to simulate the static and eigenvalue problems of the beam under various DC actuation scenarios. The model is validated by comparing with a finite element model and with experimental data. The experiments are based on in-plane silicon devices. The micro-beams are sandwiched between four electrodes (four ports) with uniform airgap for various electrostatic actuation options. These electrodes not only offer various electrostatic actuation options, but also allow the detection of the three lowest symmetric and anti-symmetric resonance frequencies. Results are presented for several case studies of micro-beams resonators of various geometrical parameters and airgap dimensions. With various actuation options and different V-shaped configurations, the structure may show only pull-in instability, the snap-through buckling, or both instabilities together. The results enable careful characterization of the snap-through buckling with the ability of increasing the static deflection range before pull-in. Also, the results can be promising for the realization of different wide–range tunable micro-resonator and for various vibration modes. These results can be useful in micro-scale applications that can be beneficial for designing structures with low power consumption, high sensitivity, and wide tuning range.