Dynamics and global stability of beam-based electrostatic microactuators

We investigate the dynamics and global stability of a beam-based electrostatic microactuator, which is modeled as a first-order approximation of a reduced-order model (ROM) derived using the differential quadrature method (DQM). We show that the ROM dynamics is qualitatively similar to that of a higher-order approximation. We simulate the occurrence of dynamic pull-in for excitations near the first primary resonance using the finite difference method (FDM) and long-time integration. Limit-cycle solutions are obtained using the FDM, the generated frequency- and force-response curves exhibit cyclic-fold, saddle-node, and period-doubling bifurcations. We verify that symmetry breaking is not likely to occur because the orbit is already asymmetric. We identify the basin of attraction of bounded motions using various approximation levels. The simulations reveal that the erosion of the basin of attraction depends heavily on the amplitude and frequency of the AC voltage. We show that smoothness of the boundary of the basin of attraction can be lost and replaced by fractal tongues, which dramatically increase the sensitivity of the microbeam to initial conditions. According to these simulations, the locations of the two fixed points are likely to be disturbed.