Electrothermally Tuned and Electrostatically Actuated MEMS Resonators: Dynamics and Applications (original) (raw)
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Effect of Initial Curvature on the Static and Dynamic Behavior of MEMS Resonators
Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, 2017
In this paper, we investigate experimentally and analytically the effect of the initial shape, arc and cosine wave, on the static and dynamic behavior of microelectromechanical (MEMS) resonators. We show that by carefully choosing the geometrical parameters and the shape of curvature, the veering phenomenon (avoided-crossing) between the first two symmetric modes can be activated. To demonstrate this concept, we study electrothermally tuned and electrostatically driven MEMS initially curved resonators. Applying electrothermal voltage heats up the beams and then increases their curvature (stiffness) and controls their resonance frequencies. While changing the electrothermal voltage, we demonstrate high frequency tunability of arc resonators compared to the cosine-configuration resonators for the first and third resonance frequencies. For arc beams, we show that the first resonance frequency increases up to twice its fundamental value and the third resonance frequency decreases until getting very close to the first resonance frequency triggering the veering phenomenon. Around the veering regime, we study experimentally and analytically, using a reduced order model based on a nonlinear Euler-Bernoulli shallow arch beam model, the dynamic behavior of the arc beam for different electrostatic forcing.
Highly Tunable Electrothermally and Electrostatically Actuated Resonators
Journal of Microelectromechanical Systems, 2016
This paper demonstrates experimentally, theoretically, and numerically, for the first time, a widerange tunability of an in-plane clamped-clamped microbeam, bridge, resonator actuated electrothermally and electrostatically. Using both actuation methods, we demonstrate that a single resonator can be operated at a wide range of frequencies. The microbeam is actuated electrothermally, by passing a DC current through it, and electrostatically by applying a DC polarization voltage between the microbeam and the stationary electrode. We show that when increasing the electrothermal voltage, the compressive stress inside the microbeam increases, which leads eventually to its buckling. Before buckling, the fundamental frequency decreases until it drops to very low values, almost to zero. After buckling, the fundamental frequency increases, which is shown to be as high as twice the original resonance frequency. Adding a DC bias changes the qualitative nature of the tunability both before and after buckling, which adds another independent way of tuning. This reduces the dip before buckling, and can eliminate it if desired, and further increases the fundamental frequency after buckling. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and to simulation results of a multi-physics finite-element model. A good agreement is found among all the results.
Theoretical and experimental nonlinear dynamics of a clamped-clamped beam MEMS resonator
Brain Research, 2008
Microelectromechanical resonators feature nonlinear dynamic responses. A first-principles based modeling approach is proposed for a clamped-clamped beam resonator. Starting from the partial differential equation for the beam including geometric and electrostatic nonlinear effects, a reduced-order model is derived. The model captures the experimentally observed nonlinear dynamic behaviour of the resonator and allows for fast simulation and prediction of its response.
Electrothermally actuated tunable clamped-guided resonant microbeams
Mechanical Systems and Signal Processing, 2018
We present simulation and experimental investigation demonstrating active alteration of the resonant and frequency response behavior of resonators by controlling the electrothermal actuation method on their anchors. In-plane clamped-guided arch and straight microbeams resonators are designed and fabricated with V-shaped electrothermal actuators on their anchors. These anchors not only offer various electrothermal actuation options, but also serve as various mechanical stiffness elements that affect the operating resonance frequency of the structures. We have shown that for an arch, the first mode resonance frequency can be increased up to 50% of its initial value. For a straight beam, we have shown that before buckling, the resonance frequency decreases to very low values and after buckling, it increases up to twice of its initial value. These results can be promising for the realization of different wide-range tunable microresonator. The experimental results have been compared to multi-physics finite-element simulations showing good agreement among them.
Tuning the Nonlinear Behaviour of Resonant MEMS Sensors Actuated Electrically
Procedia Engineering, 2012
The objectives of this present work is to study the stability and bifurcation control of an idealized electrostatically actuated microcantilever MEMS device that can widely observe in the field MEMS application. Here, the cantilever based device has been modelled as a spring-mass-damper system considering both the linear and nonlinear spring and damper. Simultaneously, the cantilever based device is excited harmonically by applied voltages. The method of multiple scales is employed to obtain the reduced order equations in terms of amplitude and phase those are directly used to determine the approximate the solutions for different resonance conditions. The catastrophic failure of the system may occur due to the presence of saddle-node and pitchfork bifurcation points as it leads the jump phenomenon. Basins of attractions are plotted in order to find the initial condition for a specific solution in a region having more than one solution. The obtained results can successfully be used in designing the microcantilever based devices that depict typical realistic nonlinear characteristics in the field of MEMS application.
International Journal of Non-Linear Mechanics, 2017
We investigate experimentally and analytically the effect of initial shapes, arc and cosine wave, on the static and dynamic behavior of microelectromechanical systems (MEMS) arch resonators. We show that by carefully choosing the geometrical parameters and the initial shape of the arch, the veering phenomenon (avoided-crossing) among the first two symmetric modes can be strongly activated. To demonstrate this, we study electrothermally tuned and electrostatically driven initially curved MEMS resonators. Upon changing the electrothermal voltage, we demonstrate high frequency tunability of arc resonators compared to the cosine-configuration resonators for the first and third resonance frequencies. For arc beams, we show that the first resonance frequency increases up to twice its fundamental value and the third resonance frequency decreases until getting very close to the first resonance frequency triggering the veering phenomenon. Around the veering regime, we study experimentally and analytically the dynamic behavior of the arc beam for different electrostatic loads. The analytical study is based on a reduced order model of a nonlinear Euler-Bernoulli shallow arch beam model. The veering phenomenon is also confirmed through a finite-element multi-physics and nonlinear model.
Experimental and analytical study of highly tunable electrostatically actuated resonant beams
Journal of Micromechanics and Microengineering, 2015
We demonstrate theoretically and experimentally highly tunable clamped-clamped microbeam resonators actuated with electrostatic forces. Theoretically, the Galerkin procedure is used to solve for the 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 effective increase of their fundamental resonance frequencies by more than 50-80%. Excellent agreement is reported among the theoretical and experimental results.
Experimental and Theoretical Study of Two-to-One Internal Resonance of MEMS Resonators
Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, 2018
In this paper, we investigate experimentally and theoretically the two-to-one (2:1) internal resonance between the first two symmetric vibrational modes of microelectromechanical (MEMS) arch resonator electrothermally tuned and electrostatically driven. Applying electrothermal voltage across the beam anchors controls its stiffness and then its resonance frequencies. Hence the ratio between the two frequencies can be tuned to a ratio of two. Then, we study the dynamic response of the arch beam during internal resonance. In the studied case, the presence of high AC bias excitation leads to the direct simultaneous excitation of the 1 st and 3 rd frequencies in addition to the activation of the internal resonance. A reduced order model and perturbation techniques are presented to analyze the nonlinear response of the structure. In the perturbation technique, the direct excitation of the 3rd resonance frequency is taken into consideration. Results show the presence of Hopf bifurcations, which can lead to chaotic motion at higher excitation. A good agreement among the theoretical and experimental results is shown.
Sensors and Actuators A-physical, 2010
By means of a combined analytical-numerical and experimental approach, the nonlinear dynamic behavior of a clamped-clamped beam MEMS resonator has been investigated. A good qualitative correspondence between simulations and experiments has been obtained. First-principles based multiphysics modeling is applied to derive a reduced-order model of the resonator. The model includes nonlinear geometric and electrostatic effects as well as thermoelastic damping. Both simulations and experiments show hardening and softening nonlinear dynamic behavior depending on the excitation parameters. The model captures the observed nonlinear behavior qualitatively and allows for design optimization with respect to nonlinear effects.
By means of a combined analytical-numerical and experimental approach, the nonlinear dynamic behavior of a clamped-clamped beam MEMS resonator has been investigated. A good quantitative correspondence between simulations and experiments has been obtained. First-principles based multiphysics modeling is applied to derive a reduced-order model of the resonator. The model includes nonlinear geometric and electrostatic effects as well as thermoelastic damping and anchor loss. Both simulations and experiments show hardening and softening nonlinear dynamic behavior depending on the excitation parameters. The model captures the observed nonlinear behavior and allows for design optimization with respect to nonlinear effects.