The response of a micro-electro-mechanical system (MEMS) cantilever-paddle gas sensor to mechanical shock loads

Abstract

This work presents an investigation into the effect of nonlinearities on the response of a micro-electro-mechanical system gas sensor under mechanical shock and electrostatic loading. The gas sensor consists of a cantilever microbeam with a rigid microplate (micro-paddle) attached to its tip. A nonlinear Euler-Bernoulli beam theory is used to model the system, accounting for both geometric and inertia nonlinearities, in addition to the nonlinear electrostatic force used to actuate the system. The system of integro-partial-differential equations is discretized using a Galerkin procedure to extract a reduced-order model, which is then used for dynamic simulations of the system responses. The influences of the different components of nonlinearity such as geometric and inertia nonlinearities are examined. The results of the nonlinear model are compared to results obtained from linear beam theory and finite element simulations. For mechanical shock loading, both quasi-static and dynamic responses of a microbeam are considered. The effect of nonlinearity is found to be significant when the deflection of the microbeam exceeds around 30% of its length. The consequence of the large deflection is that the geometric nonlinearity has a much stronger influence on the response in comparison to the inertia nonlinearity. It is also apparent that the effect of the paddle is to enhance the dynamic, as opposed to the quasi-static, response of the microbeam to mechanical shock. For electrostatic actuation, it is found that using a nonlinear beam model to predict the pull-in and the deflection produces a slight improvement over using a linear beam model.