Nonlinear Dynamic Analysis of an Electrostatically Actuated Clamped-Clamped Beam and Excited at the Primary and Secondary Resonances.

This work investigates the primary and secondary resonances of an electrostatically excited double-clamped microbeam and its feasibility to be used for sensing applications. The sensor design can be excited directly in the vicinity of the primary and secondary resonances. This excitation mechanism would portray certain nonlinear phenomena and it would certainly lead in increasing the sensitivity of the device. To achieve this, a nonlinear beam model describing transverse deflection based on the Euler-Bernoulli beam theory was utilized. Then, a reduced-order model (ROM) considering all geometric and electrical nonlinearities was derived. Three different techniques involving time domain, fast Fourier transforms (FFTs), and frequency domain (FRCs) were used to examine the appearance of subharmonic resonance of order of one-half under various excitation waveforms. The results show that higher forcing levels and lower damping are required to activate this resonance. We note that as the forcing increases, the size of the instability region grows fast and the size of the unstable region increases rapidly. This, in fact, is an ideal place for designing bifurcation inertia MEMS sensors.

Static and Eigenvalue Analysis of Electrostatically Coupled and Tunable Shallow Micro-Arches for Sensing-Based Applications.

This paper investigated the mechanical performance of an electrostatically tunable microbeams-based resonators. The resonator was designed based on two initially-curved microbeams that are electrostatically coupled, offering the potential for improved performance compared to single-beam based resonators. Analytical models and simulation tools were developed to optimize the resonator design dimensions and to predict its performance, including its fundamental frequency and motional characteristics. The results show that the electrostatically-coupled resonator exhibits multiple nonlinear phenomena including mode veering and snap-through motion. A coexistence of two stable branches of solutions for a straight beam case was even obtained due to the direct effect of the coupling electrostatic force with the other curved beam. Indeed, the results are promising for the better performance of coupled resonators compared to single-beam resonators and offer a platform for future MEMS applications including mode-localized based micro-sensors.

Investigation into Mode Localization of Electrostatically Coupled Shallow Microbeams for Potential Sensing Applications.

With the constant need for the development of smart devices, Micro-Electro-Mechanical Systems (MEMS) based smart sensors have been developed to detect hazard materials, micro-particles or even toxic substances. Identifying small particles using such micro-engineering technology requires designing sensors with high sensitivity, selectivity and ease of integration with other electronic components. Nevertheless, the available detection mechanism designs are still juvenile and need more innovative ideas to be even more competitive. Therefore, this work aims to introduce a novel, smart and innovative micro-sensor design consisting of two weakly electrostatically coupled microbeams (both serving as sensors) and electrically excited using a stationary electrode assuming a dc/ac electric signal. The sensor design can be tuned from straight to eventually initially curved microbeams. Such an arrangement would develop certain nonlinear phenomena, such as the snap-through motion. This behavior would portray certain mode veering/mode crossing and ultimately mode localization and it would certainly lead in increasing the sensitivity of the mode-localized based sensing mechanism. These can be achieved by tracking the change in the resonance frequencies of the two microbeams as the coupling control parameter is varied. To this extent, a nonlinear model of the design is presented, and then a reduced-order model considering all geometric and electrical nonlinearities is established. A Long-Time Integration (LTI) method is utilized to solve the static and dynamics of the coupled resonators under primary lower-order and higher-order resonances, respectively. It is shown that the system can display veering and mode coupling in the vicinity of the primary resonances of both beams. Such detected modal interactions lead to an increase in the sensitivity of the sensor design. In addition, the use of two different beam's configurations in one device uncovered a possibility of using this design in detecting two potential substances at the same time using the two interacting resonant peaks.

Nonlinear Parameter Identification of a Resonant Electrostatic MEMS Actuator.

We experimentally investigate the primary superharmonic of order two and subharmonic of order one-half resonances of an electrostatic MEMS actuator under direct excitation. We identify the parameters of a one degree of freedom (1-DOF) generalized Duffing oscillator model representing it. The experiments were conducted in soft vacuum to reduce squeeze-film damping, and the actuator response was measured optically using a laser vibrometer. The predictions of the identified model were found to be in close agreement with the experimental results. We also identified the noise spectral density of process (actuation voltage) and measurement noise.