A MEMS device electrically actuated: Global dynamics and dynamical integrity

This study deals a MEMS device, which consists of a shallow arched microbeam, with axial load deliberately added and electrostatic and electrodynamic actuation. The microstructure is characterized by a bistable static configuration. A single degree of freedom model is derived and extensive numerical simulations are performed. They highlight a considerable versatility of behavior, which may have many feasible applications. After analyzing the attractors coexisting in each parameter range, we focus on each rest position, and we investigate the final outcome, when the electrodynamic voltage is suddenly applied. Our aim is to describe if the suddenly applied electric load will lead to dynamic pull-in or to a bounded motion. To summarize the overall scenario, we build the theoretical charts. They illustrate the final response, when, starting from each rest position, the microstructure is suddenly excited with different values of frequency and electrodynamic voltage. Nevertheless, these results represent a theoretical limit, which never occurs in practice. This is because, under realistic conditions, disturbances exist and are unavoidable, as, for instance, the noise from the pump, a transient not completely removed, imperfections due to the microfabrication, etc. Disturbances give uncertainties to the operating initial conditions, which may lead to an outcome different from what theoretically predicted. In the literature, a similar discrepancy has been highlighted in many different dynamical systems. To take disturbances into account, a dynamical integrity analysis is performed. After introducing the dynamical integrity tools of safe basin and integrity measure, for each initial condition of rest we examine the practical vulnerability to dynamic pull-in. This is performed via integrity profiles and integrity charts. A small integrity enhances the sensitivity of the system to disturbances. Consequently, the parameter range where the device, subjected to a suddenly applied load, can operate in safe conditions is smaller, and, sometimes, considerably smaller, than in the theoretical predictions. The obtained integrity charts are able to provide quantitative information about the changes in the structural safety. They may be used in the engineering design to establish safety factors and operate the device according to the desired behavior.