Dynamics of a clamped–clamped microbeam resonator considering fabrication imperfections

We present an investigation into the static and dynamic behavior of an electrostatically actuated clamped–clamped polysilicon microbeam resonator accounting for its fabrication imperfections, which are commonly encountered in similar microstructures. These are mainly because of the initial deformation of the beam due to stress gradient and its flexible anchors. First, we show experimental data of the microbeam when driven electrically by varying the amplitude and frequency of the voltage loads. The results reveal several interesting nonlinear phenomena of jumps, hysteresis, and softening behaviors. Theoretical investigation is then conducted to model the microbeam, and hence, interpret the experimental data. We solve the Eigen value problem governing the natural frequencies analytically. We then utilize a Galerkin-based procedure to derive a reduced order model, which is then used to simulate both the static and dynamic responses. To achieve good matching between theory and experiment, we show that the exact profile of the deformed beam needs to be utilized in the reduced order model, as measured from the optical profiler, combined with a shooting technique simulation, which is capable of tracing the resonant frequency branches under very-low damping conditions.