The present research study deals with an electrically actuated MEMS device. An experimental investigation is performed, via frequency sweeps in a neighbourhood of the first natural frequency. Resonant behavior is explored, with special attention devoted to jump and pull-in dynamics. A theoretical single degree-of-freedom spring-mass model is derived. Classical numerical simulations are observed to properly predict the main nonlinear features. Nevertheless, some discrepancies arise, which are particularly visible in the resonant branch. They mainly concern the practical range of existence of each attractor and the final outcome after its disappearance. These differences are likely due to disturbances, which are unavoidable in practice, but have not been included in the model. To take disturbances into account, in addition to the classical local investigations, we consider the global dynamics and explore the robustness of the obtained results by performing a dynamical integrity analysis. Our aim is that of developing an applicable confident estimate of the system response. Integrity profiles and integrity charts are built to detect the parameter range where reliability is practically strong and where it becomes weak. Integrity curves exactly follow the experimental data. They inform about the practical range of actuality. We discuss the combined use of integrity charts in the engineering design. Although we refer to a particular case-study, the approach is very general.

This work investigates the dynamics of a microbeam-based MEMS device in the neighborhood of a 2:1 internal resonance between the third and fifth vibration modes. The saturation of the third mode and the concurrent activation of the fifth are observed. The main features are analyzed extensively, both experimentally and theoretically. We experimentally observe that the complexity induced by the 2:1 internal resonance covers a wide driving frequency range. Constantly comparing with the experimental data, the response is examined from a global perspective, by analyzing the attractor-basins scenario. This analysis is conducted both in the third-mode and in fifth-mode planes. We show several metamorphoses occurring as proceeding from the principal resonance to the 2:1 internal resonance, up to the final disappearance of the resonant and non-resonant attractors. The shape and wideness of all the basins are examined. Although they are progressively eroded, an appreciable region is detected where the compact cores of the attractors involved in the 2:1 internal resonance remain substantial, which allows effectively operating them under realistic conditions. The dynamical integrity of each resonant branch is discussed, especially as approaching the bifurcation points where the system becomes more vulnerable to the dynamic pull-in instability.

A new multi-sensing scheme via nonlinear weakly coupled resonators is introduced in this paper, which can simultaneously detect two different physical stimuli by monitoring the dynamic response around the first two lowest modes. The system consists of a mechanically coupled bridge resonator and cantilever resonator. The eigenvalue problem is solved to identify the right geometry for the resonators to optimize their resonance frequencies based on mode localization in order to provide outstanding sensitivity. A nonlinear equivalent model is developed using the Euler–Bernoulli beam theory while accounting for the geometric and electrostatic nonlinearities. The sensor's dynamics are explored using a reduced-order model based on two-mode Galerkin discretization, which reveals the richness of the response. To demonstrate the proposed sensing scheme, the dynamic response of the weakly coupled resonator is investigated by tuning the stiffness and mass of the bridge and cantilever resonators, respectively. With its simple and scalable design, the proposed system shows great potential for intelligent multi-sensing detection in many applications.