Size-Dependent Dynamic Behavior of Electrostatically Actuated Microaccelerometers Under Mechanical Shock

This paper studies the size-dependent dynamic behavior of electrostatically actuated micro-accelerometers using the modified couple stress theory. The device is modeled as a cantilevered microbeam with an electrostatically actuated proof mass attached to its free end. The equation of motion is derived based on the Hamilton's principle and solved both numerically (using the finite element and finite difference methods) and analytically (using the perturbation technique) and the dynamic response and pull-in instability of the device is studied. The results of these methods are compared and the source of error in the analytical results at high values of external acceleration is discussed. Furthermore, the results are compared with those evaluated based on the classical theory. It is found that for cantilevered accelerometers with a beam thickness of the order of the material length scale parameter, the classical theory gives a rough estimation of the dynamic response of the system. In this situation, the error of using the classical theory may change the prediction of the system behavior from unstable to stable.