Modeling and analysis of a capacitive MEMS with a microstructured gap subjected to a mechanical shock

The objective of this paper is to present a mathematical model for examining the response of capacitive MEMS with elastomeric microstructured gaps, to mechanical shock pulses. This type of MEMS has attracted increasing attention in recent years due to its enhanced sensitivity, particularly in healthcare systems. Although the literature successfully develops experimental analysis, it lacks a comprehensive mathematical model to predict behavior, as well as necessary analysis. This paper presents a model that focuses on the response of a half-sine shock. The capacitor gap has been filled with a micro-pillar array made of polydimethylsiloxane (PDMS) as a microstructured layer. Three sets of coupled nonlinear differential equations have been obtained to govern the transverse vibrations of the beam, and the axial and bending vibrations of the pillars. PDMS has been assumed to follow the Kelvin–Voigt model, along with the nonlinear strain. A comparison was made between the air and PDMS gap systems, revealing that the former experiences a response amplitude several times smaller than the latter due to the added stiffness of the pillars in the absence of an electrostatic field. Nevertheless, when the electrostatically actuated beam is subjected to shock, the opposite results may be observed. This is due to the opposing effects of the added stiffness of the pillars and the gap’s higher permittivity. The results demonstrate that the provided model is capable of accurately predicting the response of the microstructured-gap capacitor to mechanical shocks and other external stimuli.