Voltage and Deflection Amplification via Double Resonance Excitation in a Cantilever Microstructure

Cantilever electrostatically-actuated resonators show great promise in sensing and actuating applications. However, the electrostatic actuation suffers from high-voltage actuation requirements and high noise low-amplitude signal-outputs which limit its applications. Here, we introduce a mixed-frequency signal for a cantilever-based resonator that triggers its mechanical and electrical resonances simultaneously, to overcome these limitations. A single linear RLC circuit cannot completely capture the response of the resonator under double resonance excitation. Therefore, we develop a coupled mechanical and electrical mathematical linearized model at different operation frequencies and validate this model experimentally. The double-resonance excitation results in a 21 times amplification of the voltage across the resonator and 31 times amplitude amplification over classical excitation schemes. This intensive experimental study showed a great potential of double resonance excitation providing a high amplitude amplification and maintaining the linearity of the system when the parasitic capacitance is maintained low

Parametric Resonance of a Repulsive Force MEMS Electrostatic Mirror

We investigate the nonlinear dynamic behavior of an electrostatic MEMS mirror. The MEMS mirror is driven by repulsive force actuators, which avoid pull-in instability and enable large travel ranges. In parallel-plate actuators, the force on the structure is toward the substrate limiting the range of motion to the capacitor gap. Unlike parallel-plate, repulsive force actuators push the mirror away from the substrate not limiting the motion. The highly nonlinear nature of the repulsive force and the large motions create unique characteristics that dier from parallel-plate actuators. Repulsive force actuators show linear natural frequency hardening with increased DC voltages unlike parallel-plate ones that have frequency softening. A large parametric resonance is another attribute of repulsive force actuators as the limitations of a small gap and pull-in instability are eliminated. To simulate the system response, we use a lumped parameter model with linear and cubic stiness modulated by the excitation voltage that causes parametric resonances. Using the shooting technique, we obtained simulations that agree well with the nonlinear responses observed in our experiments. As the limitation of a small gap is overcome, the electrostatic force triggers large principal parametric resonances with amplitudes as large as the primary resonance. The parametric resonance is more pronounced at low DC excitation levels when geometric nonlinearities are not significant (axial stress is low). While the initial gap is only 2 microns, under parametric resonance, our one-millimeter diameter mirror reaches 43 m at 1.2 KHz when the excitation level is as low as VDC = 40 V; VAC = 1 V in a vacuum. The ability to achieve parametric resonances with repulsive force actuation can serve and improve the signal-to-noise ratio and speed in various applications such as confocal microscopy

Theoretical Prediction of Experimental Jump and Pull-In Dynamics in a MEMS Sensor

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

Voltage and Deflection Amplification via Double Resonance Excitation in a Cantilever Microstructure

Cantilever electrostatically-actuated resonators show great promise in sensing and actuating applications. However, the electrostatic actuation suffers from high-voltage actuation requirements and high noise low-amplitude signal-outputs which limit its applications. Here, we introduce a mixed-frequency signal for a cantilever-based resonator that triggers its mechanical and electrical resonances simultaneously, to overcome these limitations. A single linear RLC circuit cannot completely capture the response of the resonator under double resonance excitation. Therefore, we develop a coupled mechanical and electrical mathematical linearized model at different operation frequencies and validate this model experimentally. The double-resonance excitation results in a 21 times amplification of the voltage across the resonator and 31 times amplitude amplification over classical excitation schemes. This intensive experimental study showed a great potential of double resonance excitation providing a high amplitude amplification and maintaining the linearity of the system when the parasitic capacitance is maintained low

Voltage and Deflection Amplification via Double Resonance Excitation in a Cantilever Microstructure

Cantilever electrostatically-actuated resonators show great promise in sensing and actuating applications. However, the electrostatic actuation suffers from high-voltage actuation requirements and high noise low-amplitude signal-outputs which limit its applications. Here, we introduce a mixed-frequency signal for a cantilever-based resonator that triggers its mechanical and electrical resonances simultaneously, to overcome these limitations. A single linear RLC circuit cannot completely capture the response of the resonator under double resonance excitation. Therefore, we develop a coupled mechanical and electrical mathematical linearized model at different operation frequencies and validate this model experimentally. The double-resonance excitation results in a 21 times amplification of the voltage across the resonator and 31 times amplitude amplification over classical excitation schemes. This intensive experimental study showed a great potential of double resonance excitation providing a high amplitude amplification and maintaining the linearity of the system when the parasitic capacitance is maintained low

Theoretical prediction of experimental jump and pull-in dynamics in a MEMS sensor

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

Nonlinear Dynamics of an Electrically Actuated MEMS Device: Experimental and Theoretical Investigation

This study deals with an experimental and theoretical investigation of an electrically actuated micro-electro-mechanical system (MEMS). The experimental nonlinear dynamics are explored via frequency sweeps in a neighborhood of the first symmetric natural frequency, at increasing values of electrodynamic excitation. Both the non-resonant branch, the resonant one, the jump between them, and the presence of a range of inevitable escape (dynamic pull-in) are observed. To simulate the experimental behavior, a single degree-of-freedom spring mass model is derived, which is based on the information coming from the experimentation. Despite the apparent simplicity, the model is able to catch all the most relevant aspects of the device response. This occurs not only at low values of electrodynamic excitation, but also at higher ones. 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, under realistic conditions, disturbances are inevitably encountered (e.g. discontinuous steps when performing the sweeping, approximations in the modeling, etc.) and give uncertainties to the operating initial conditions. A reliable prediction of the actual (and not only theoretical) response is essential in applications. To take disturbances into account, we develop a dynamical integrity analysis. Integrity profiles and integrity charts are performed. They are able to detect the parameter range where each branch can be reliably observed in practice and where, instead, becomes vulnerable. Moreover, depending on the magnitude of the expected disturbances, the integrity charts can serve as a design guideline, in order to effectively operate the device in safe condition, according to the desired outcome