Theoretical and experimental investigation of dynamic instabilities in electrostatic MEMS

We present modeling, analysis, and experimental investigation for dynamic instabilities and bifurcations in electrostatic Micro-electro-mechanical systems (MEMS). These instabilities are induced by exciting a microstructure with a nonlinear forcing composed of a DC parallel-plate electrostatic load and an AC harmonic load. The frequency of the AC load is tuned to be near and twice the fundamental natural frequency of the structure. For this excitation method, several local bifurcations, such as saddle-node and pitchfork, and global bifurcations, such as the escape phenomenon and the homoclinic tangling occur. These lead to undesirable jumps, hysteresis, and dynamic pull-in instabilities in MEMS devices and structures. In this work, simulation results will be shown for micro-scale cantilever microbeams that illustrate the global bifurcation such as the escape phenomenon around the primary and the subharmonic resonances. The simulations results are obtained by long-time integration for the equation of motion of a reduced-order beam model. Then, theoretical and experimental investigation will be presented demonstrating these instabilities for a mille-micro-scale capacitive sensor. Experimental data for dynamic pull-in will be shown for the case of the primary excitations.