Nonlinear dynamics of a MEMS resonator: Theoretical and experimental investigation

In this study we present a theoretical and experimental investigation of a microelectromechanical system (MEMS). The device is constituted of a clamped-clamped polysilicon microbeam electrostatically and electrodynamically actuated. The microbeam has a slightly curled up configuration, which is an imperfection commonly encountered as a consequence of the microfabrication process. Using a laser Doppler vibrometer, many experimental frequency sweeps are conducted in a neighborhood of the first symmetric natural frequency. To simulate the dynamics, we derive a single-mode reduced-order model. Extensive numerical investigations are performed, based on frequency response diagrams and behavior charts. The overall scenario of the response is explored, when both the frequency and the electrodynamic voltage are varying. This analysis is able to provide a very good matching with the experiments. Nevertheless, the theoretical predictions are not completely fulfilled in some aspects. In particular, the range of existence of each attractor is smaller in practice than in the simulations. This is because the theoretical curves represent the ideal limit case where disturbances are absent, which never occurs in experiments and practice. To overcome this drawback and extend the results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After introducing dynamical integrity concepts, we perform integrity profiles and integrity charts. They are able to describe if each attractor is robust enough to tolerate the disturbances. They detect the parameter range where each branch can be reliably observed in practice and where, instead, becomes vulnerable, i.e., depending on the expected disturbances, they provide valuable information to operate the device in safe conditions according to the desired outcome.