Shape Optimization of Electrostatically Actuated Microbeams With Extended Static and Dynamic Operating Ranges

Abstract

We present a generic shape optimization methodology to maximize the static and dynamic pull–in ranges of electrostatically actuated microbeams. Energy based techniques are used to extract the static and dynamic pull–in parameters. A versatile parametric width function is used to characterize nonprismatic geometries, and the parameters of the proposed width function are optimized using the Nelder–Mead method of function minimization together with a penalty method to enforce the constraints. The constraints that we consider are encountered in typical microbeam applications. We consider matrix of several test cases in order to fully demonstrate the utility of the proposed methodology. Our results indicate that an increase in the pull–in displacement of as much as 19% can be obtained using our optimization approach. We present optimal shapes of these microbeams, that easily lend themselves to microfabrication, which exhibit the improved pull–in response in both static and dynamic regimes.