Nonlinear analysis and characteristics of electrically-coupled microbeams under mechanical shock

Several studies have shown that MEMS devices deploying electrically-actuated vibrating beams, such as resonant sensors and RF filters may fail to operate when undergoing mechanical shocks due to the pull-in instability. To this end, we investigate the possibility to overcome or exploit this issue by considering different microsystem designs based on the application of interest. This objective is carried out through developing a nonlinear reduced-order model to simulate the dynamic response of single and dual microbeams under varying electric actuation and shock loads. The actuation of the single-beam system is made via a fixed electrode (uncoupled actuation) while the dual-beam system, composed of two movable microbeams, is actuated by applying a voltage among them (coupled actuation). We use the Galerkin method to discretize the governing equations in space and the Runge–Kutta method to integrate the resulting nonlinear ordinary differential equations. We first perform the static analysis to determine the pull-in voltage. We formulate the coupled eigenvalue problem to compute the natural frequencies of the microsystems under investigation for different applied DC voltages. Then, we introduce the AC excitation and generate the frequency-response curves. Finally, we analyze the impact of the mechanical shock (represented by an impact pulse acceleration) on the microsystems’ dynamic behavior. The present results are in good agreement with those obtained from previously-published theoretical and experimental studies. We observe a significant reduction in the static pull-in voltage and switching time when considering the dual-beam system in comparison with the single-beam case. The frequency-response curves show expanded dynamic pull-in bandwidth when operating the dual-beam system near the primary resonance. We notice that the dual-beam systems are more robust in terms of resistance to mechanical shock. This shows the suitability of such design for the operation and reliability of MEMS devices in harsh environments characterized by high mechanical shock levels. On the other hand, single-beam systems seem to be more attractive for use as microswitches which are intended to trigger a signal once receiving a mechanical shock or abrupt change in acceleration to activate safety functionalities, such as airbag systems.