Abdallah Ramini

An Experimental and Theoretical Investigation of a Micromirror Under Mixed-Frequency Excitation

We present an experimental and theoretical investigation of a micromachined mirror under a mixed-frequency signal composed of two harmonic ac sources. The micromirror is made of polyimide as the main structural layer. The experimental and theoretical dynamics are explored via frequency sweeps in the desired neighborhoods. One frequency is fixed while the other frequency is swept through a wide range to study the dynamic responses. To simulate the behavior of the micromirror, it is modeled as a single degree of freedom system, where the parameters of the model are extracted experimentally. A good agreement is reported among the simulation results and the experimental data. These responses are studied under different frequencies and input voltages. The results show interesting dynamics, where the system exhibits primary resonance and combination resonances of additive and subtractive type. The mixed excitation is demonstrated as a way to increase the bandwidth of the resonator near primary resonance, which can be promising for resonant sensing applications in the effort to increase the signal-noise ratio over extended frequency range.

A low-g electrostatically actuated resonant switch

This work investigates a new concept of an electrostatically actuated resonant switch (EARS) for earthquake detection and low-g seismic applications. The resonator is designed to operate close to the instability bands of frequency?response curves, where it is forced to collapse dynamically (pull-in) if operated within these bands. By careful tuning, the resonator can be made to enter the pull-in instability zone upon the detection of the earthquake signal, thereby snapping down as an electric switch. Such a switching action can be functionalized for alarming purposes or can be used to activate a network of sensors for seismic activity recording. The EARS is modeled and its dynamic response is simulated using a nonlinear single-degree-of-freedom model. Experimental investigation is conducted demonstrating the EARS? capability of being triggered at small levels of acceleration as low as 0.02g. Results for the switching events for several levels of low-g accelerations using both theory and experiments are presented and compared.

Higher order modes excitation of electrostatically actuated clamped–clamped microbeams: experimental and analytical investigation

In this study, we demonstrate analytically and experimentally the excitations of the higher order modes of vibrations in electrostatically actuated clamped–clamped microbeam resonators. The concept is based on using partial electrodes with shapes that induce strong excitation of the mode of interest. The devices are fabricated using polyimide as a structural layer coated with nickel from the top and chrome and gold layers from the bottom. Experimentally, frequency sweeps with different electro-dynamical loading conditions are shown to demonstrate the excitation of the higher order modes of vibration. Using a half electrode, the second mode is excited with high amplitude of vibration compared with almost zero response using the full electrode. Also, using a two-third electrode configuration is shown to amplify the third mode resonance amplitude compared with the full electrode under the same electrical loading conditions. An analytical model is developed based on the Euler–Bernollui beam model and the Galerkin method to simulate the device response. Good agreement between the simulation results and the experimental data is reported.

Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch

We present theoretical and experimental investigation of the nonlinear behavior of a clamped-clamped in-plane microelectromechanical systems (MEMS) arch when excited by a dc electrostatic load superimposed to an ac harmonic load. Experimentally, a case study of in-plane silicon micromachined arch is examined and its mechanical behavior is measured using the optical techniques. An algorithm is developed to extract the various parameters, such as the induced axial force and the initial rise, needed to model the behavior of the arch. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. In addition, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Dynamic snap-through behavior is also reported for the larger range of electric loads. Theoretically, a multi-mode Galerkin reduced order model is utilized to simulate the arch behavior. General agreement is reported among the theoretical and experimental data.

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.

Tunable Clamped–Guided Arch Resonators Using Electrostatically Induced Axial Loads

We present a simulation and experimental investigation of bi-directional tunable in-plane clamped–guided arch microbeam resonators. Tensile and compressive axial forces are generated from a bi-directional electrostatic actuator, which modulates the microbeam stiffness, and hence changes its natural frequency to lower or higher values from its as-fabricated value. Several devices of various anchor designs and geometries are fabricated. We found that for the fabricated shallow arches, the effect of the curvature of the arch is less important compared to the induced axial stress from the axial load. We have shown that the first mode resonance frequency can be increased up to twice its initial value. Additionally, the third mode resonance frequency can be increased up to 30% of its initial value. These results can be promising as a proof-of-concept for the realization of wide-range tunable microresonators. The experimental results have been compared to finite-element simulations, showing good agreement among them.

Experimental investigation of snap-through motion of in-plane MEMS shallow arches under electrostatic excitation

We present an experimental investigation for the nonlinear dynamic behaviors of clamped–clamped in-plane MEMS shallow arches when excited by harmonic electrostatic forces. Frequency sweeps are conducted to study the dynamic behaviors in the neighborhoods of the first and third resonance frequencies as well as the super-harmonic resonances. Experimental results show local softening behavior of small oscillations around the first resonance frequency and hardening behavior at the third resonance frequency for small dc and ac loads. Interesting dynamic snap-through cross-well motions are observed experimentally at high voltages for the first time in the micro-scale world. In addition to the dynamic snap-through motion, the MEMS arch exhibits large oscillations of a continuous band of snap-through motion between the super-harmonic resonance regime and the first primary resonance regime. This continuous band is unprecedented experimentally in the micro/macro world, and is promising for a variety of sensing, actuation and communications applications.

Experimental and analytical study of highly tunable electrostatically actuated resonant beams

We demonstrate theoretically and experimentally highly tunable clamped–clamped microbeam resonators actuated with electrostatic forces. Theoretically, the Galerkin procedure is used to solve for static deflection as well as the eigenvalue problem as a function of the dc voltage for different values of the ratio between the air gap and the thickness of the microbeam. We demonstrate theoretically and experimentally that the natural frequency of the microbeam can increase or decrease with the increase of the dc polarization voltage depending on the ratio between the air gap and the thickness. Hence, we show that unlike the classical softening effect of the dc voltage, by careful designs of the microbeams, the dc bias can be used to effectively increase the resonance frequencies by several factors. Experimental data are presented for two case studies of silicon beams showing the effective increase of their fundamental resonance frequencies by more than 50–80%. Excellent agreement is reported among the theoretical and experimental results.

Tunable Resonators for Nonlinear Modal Interactions.

Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.

In-Plane MEMS Shallow Arch Beam for Mechanical Memory

We demonstrate a memory device based on the nonlinear dynamics of an in-plane microelectromechanical systems (MEMS) clamped–clamped beam resonator, which is deliberately fabricated as a shallow arch. The arch beam is made of silicon, and is electrostatically actuated. The concept relies on the inherent quadratic nonlinearity originating from the arch curvature, which results in a softening behavior that creates hysteresis and co-existing states of motion. Since it is independent of the electrostatic force, this nonlinearity gives more flexibility in the operating conditions and allows for lower actuation voltages. Experimental results are generated through electrical characterization setup. Results are shown demonstrating the switching between the two vibrational states with the change of the direct current (DC) bias voltage, thereby proving the memory concept.