Parameter identification of an electrically actuated imperfect microbeam

In this study we consider a microelectromechanical system (MEMS) and focus on extracting analytically the model parameters that describe its non-linear dynamic features accurately. The device consists of a clamped-clamped polysilicon microbeam electrostatically and electrodynamically actuated. The microbeam has imperfections in the geometry, which are related to the microfabrication process, resulting in many unknown and uncertain parameters of the device. The objective of the present paper is to introduce a simple but appropriate model which, despite the inevitable approximations, is able to describe and predict the most relevant aspects of the experimental response in a neighborhood of the first symmetric resonance. The modeling includes the main imperfections in the microstructure. The unknown parameters are settled via parametric identification. The approach is developed in the frequency domain and is based on matching both the frequency values and, remarkably, the frequency response curves, which are considered as the most salient features of the device response. Non-linearities and imperfections considerably complicate the identification process. Via the combined use of linear analysis and non-linear dynamic simulations, a single first symmetric mode reduced-order model is derived. Extensive numerical simulations are performed at increasing values of electrodynamic excitation. Comparison with experimental data shows a satisfactory concurrence of results not only at low electrodynamic voltage, but also at higher ones. This validates the proposed theoretical approach. We highlight its applicability, both in similar case-studies and, more in general, in systems.