Nonlinear Analysis of Electrically-coupled Microbeams under Mechanical Shock

Abstract

This work presents a theoretical investigation of the dynamic response of electrically-coupled microcantilever beams under the combined effect of squeeze-film damping and mechanical shock for MEMS applications. Several research studies have reported and analyzed the failure of MEMS devices deploying electrically-actuated vibrating beams, such as inertial, bio-mass, and gas sensors, when undergoing mechanical shocks due to the inherent pull-in instability. The sensitivity of the vibrating beams to mechanical shock can also be exploited to design microswitches that are intended to trigger a signal once receiving a mechanical shock to activate safety functionalities, such as airbag systems. We consider two different microsystem designs, namely: single and dual beams, operating at varying conditions. The single-beam system is actuated via a fixed electrode (uncoupled actuation) while the electric actuation of the dual-beam system, comprising two movable microbeams, is achieved by applying a DC and AC voltages among them (coupled actuation). We develop a mathematical model to simulate the dynamic response of the single and dual microbeams while accounting for the Fringing field effect, the squeeze-film damping, and the mechanical shock. The simulation results are in good qualitative and quantitative agreement with those reported in the literature. A parametric study is conducted to investigate the effect of the electric actuation, the initial gap distance, the fluid viscosity, and the beam geometry on the shock response of the microsystem. We observe a significant reduction of 29-36% in the pull-in voltage 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 symmetric 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. Breaking the symmetry of the dual beam system in terms of the beams’ geometry is found to significantly reduce the resistance to shocks. Given their high sensitivity to mechanical shock, single-beam systems are observed to be more attractive for deployment as microswitches.