Shock response of electrostatically coupled microbeams under the squeeze-film damping effect

This paper presents a theoretical investigation of the dynamic response of electrostatically coupled microcantilever beams under the combined effect of squeeze-film damping and mechanical shock for MEMS applications. We consider two different microsystem designs, namely single and dual beams, operating at varying conditions to explore their possible use based on the application of interest. 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 voltage among them (coupled actuation). We develop a multi-physics model to simulate the dynamic response of single and dual microbeams while accounting for the fringing field effect, the squeeze-film damping resulting from the interactions between the vibrating microbeams and the surrounding fluid, and the mechanical shock. The squeeze-film damping is incorporated using a nonlinear analytical expression rather than solving the fully coupled fluid–structure problem. Numerous studies have shown the validity of this analytical approach under the assumption of long beams and neglecting the fluid compressibility. Some benchmark cases are considered to verify the predictive capability of the numerical model. The simulation results are in good qualitative and quantitative agreements with those reported in the literature. A parametric study is then conducted to investigate the effects of the initial gap distance, the fluid viscosity, and the beam geometry on the shock response of the microsystem. The squeeze-film damping enables the protection of the vibrating microbeams from hitting the substrate under mechanical shock and can be exploited to enhance the reliability of MEMS devices. However, this protection can be significantly reduced by increasing the gap distance or decreasing the operating pressure. The numerical study shows that the dual-beam systems withstand better to a mechanical shock. Breaking the symmetry of the dual-beam system in terms of the beams’ geometry is found to reduce significantly the resistance to shocks. On the other hand, given their high sensitivity to a mechanical shock, single-beam systems are observed to be more attractive for deployment as microswitches.