Abstract
In this paper, we present a theoretical and experimental investigation into the dynamic response of an electrostatically actuated microbeam when subjected to drop-table test. For the theoretical part, a reduced-order model based on an Euler-Bernoulli beam model is utilized. The model accounts for the electrostatic bias on the microbeam and the shock pulse of the drop-table test. Simulation results are presented showing the combined effect of electrostatic force and mechanical shock in triggering early pull-in instability of the cantilever microbeams. The analytical simulation results are validated by finite-element results for the static response. Dynamic pull-in threshold as a function of the mechanical shock amplitude is shown over a wide range of shock spanning hundreds of thousands of g up to zero g. For the experimental part, a micromachined cantilever beam made of gold of length 50 µm is subjected to drop-table tests while being biased by electrostatic loads. Several experimental data are shown demonstrating the phenomenon of collapse due to the combined shock and electrostatic forces. It is also demonstrated that by biasing short and too stiff microbeams with electrostatic voltages, their stiffness is weakened. This lowers their threshold of collapse considerably to the range of acceleration that enables testing them with in-house shock testing equipments, such as drop-table tests.