Fringing Electrostatic Field Actuation of Microplates for Open Air Environment Sensing

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Avinoam Rabinovich ◽  
Assaf Ya'akobovitz ◽  
Slava Krylov

In the present study, we tested the feasibility of actuation of microplates by fringing electrostatic fields, i.e., field lines between plates and the sidewalls supporting them. Unlike the common close-gap actuation mechanism usually used in these kinds of devices, we present an alternative operational principle based on an electrostatic fringe field for the actuation of micro electromechanical (MEMS) plates, which is especially beneficial for open air environment operation. In order to validate the actuation principle, a circular MEMS plate was considered and an analytical model was built. The electrostatic force applied to the plate was extracted from a solution of a steady boundary value problem of a cylinder and was validated numerically using finite element simulation. This was followed by a solution of the plate governing equation of motion using an expansion theorem. Devices of two different geometries were fabricated and operated. Actuation of the plates by means of the fringing field was demonstrated experimentally. The proposed architecture and actuation principle is advantageous and overcomes many of the difficulties encountered in microplates electrostatically actuated by a close-gap electrode. Due to the absence of a small gap, the device is not prone to pull-in instability and stiction and is not subjected to squeeze-film damping. Moreover, since the actuation is separated from the front side of the device, open air contaminations, such as humidity or dust, cannot cause operational failure. In addition, the device is especially beneficial for mass sensing in an open environment, as well as flow senors where a flush-mounted smooth surface is important.

2010 ◽  
Vol 17 (6) ◽  
pp. 759-770 ◽  
Author(s):  
Wen-Ming Zhang ◽  
Guang Meng ◽  
Ke-Xiang Wei

In this paper, nonlinear dynamics and chaos of electrostatically actuated MEMS resonators under two-frequency parametric and external excitations are investigated analytically and numerically. A nonlinear mass-spring-damping model is used to accounting for squeeze film damping and the parallel plate electrostatic force. The micro-structure is excited by a dc bias electrostatic force and a harmonic force with a frequency tuned closely to their fundamental natural frequencies (combination oscillation). The quality factor is calculated for the microcantilever beam of the resonator considering squeeze film damping. The effect of nonlinear squeeze film damping on the frequency response, quality factor, resonant frequency and nonlinear dynamic characteristics of the dynamic system are provided with numerical simulations using the bifurcation diagram, Poicare maps, largest Lyapunov exponent and phase portrait. The results show that the dynamic system goes through a complex nonlinear vibration as the system parameters change. It is indicated that the effect of nonlinear squeeze film damping should be considered due to its decreasing the quality factor and changing the nonlinear phenomena of the MEMS resonators.


2007 ◽  
Vol 2 (3) ◽  
pp. 232-241 ◽  
Author(s):  
Mohammad I. Younis ◽  
Ali H. Nayfeh

We present a new method for simulating squeeze-film damping of microplates actuated by large electrostatic loads. The method enables the prediction of the quality factors of microplates under a limited range of gas pressures and applied electrostatic loads up to the pull-in instability. The method utilizes the nonlinear Euler-Bernoulli beam equation, the von Kármán plate equations, and the compressible Reynolds equation. The static deflection of the microplate is calculated using the beam model. Analytical expressions are derived for the pressure distribution in terms of the plate mode shapes around the deflected position using perturbation techniques. The static deflection and the analytical expressions are substituted into the plate equations, which are solved using a finite-element method. Several results are presented showing the effect of the pressure and the electrostatic force on the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors.


Author(s):  
Mahmoud I. Ibrahim ◽  
Mohammad I. Younis

This paper presents a theoretical and experimental investigation on the effects of squeeze film damping and electrostatic forces on the shock spectrum of a capacitive accelerometer. For the theoretical part, a single-degree-of-freedom system is used to model the device. Simulation results are demonstrated in a series of shock spectra that help indicate the nonlinear effects on the motion of a MEMS device. When squeeze-film effects are absent, the electrostatic forces soften the microstructure and increase its deflection significantly. A range of shock durations was found in which the microstructure experiences pull-in (pull-in zone). Larger pull-in zones are obtained as we raise the electrostatic force. On the other hand, the presence of squeeze film highly suppresses the deflection of the microstructure in the dynamic range and has minor effects in the quasi-static range. It is found in the other case that the microstructure experiences pull-in in the quasi-static range. Simulation results are compared to experimental data, showing excellent agreement.


Author(s):  
S. Ahmad Tajalli ◽  
Mahdi Moghimi Zand ◽  
Mohammad Taghi Ahmadian

In this paper, dynamic behavior and pull-in phenomenon of electrically actuated rectangular micro plates under the effect of squeeze-film damping and nonlinear electrostatic force is studied. Finite element method is implemented in order to drive weak formulations of linear and nonlinear micro plate equations of motion based on classical plate theory (CPT) (for thin microplates with moderate nonlinearity) and squeeze-film damping based on Reynolds nonlinear equation. Finally, an efficient reduced-order model contingent on singular value decomposition method (SVD) is used to study dynamic pull-in phenomenon. This model is constructed by the global basis functions achieved from a few runs of FEM and can reduce simulation time. Validating the macro model results with full FEM simulation shows that this model is effective.


Author(s):  
Wen-Ming Zhang ◽  
Guang Meng ◽  
Di Chen

Electrostatically actuated resonant MEMS (Micro-electromechanical Systems) have gotten significant attention due to their geometric simplicity and broad applicability. In this paper, analyses and simulations for the dynamics of electrostatically actuated MEM structures under parametric and external excitations are presented. The presented model and methodology enable simulation of the dynamics of the electrostatic MEM structure undergoing small motions. The numerical results showing the effects of varying the applied voltages and the squeeze film damping on the resonant frequencies and nonlinear dynamic characteristics are given in detail. Resonant frequency and peak amplitude are examined for variation of the dynamical parameters involved. It is demonstrated that the system goes through a complex nonlinear oscillation as the system parameters change. This investigation provides an understanding of the nonlinear dynamic characteristics of electrostatically actuated resonant MEMS.


2013 ◽  
Vol 05 (03) ◽  
pp. 1350032 ◽  
Author(s):  
M. MOJAHEDI ◽  
M. T. AHMADIAN ◽  
K. FIROOZBAKHSH

In this paper, a nonlinear model is used to analyze the dynamic pull-in instability and vibrational behavior of a microcantilever gyroscope. The gyroscope has a proof mass at its end and is subjected to nonlinear squeeze film damping, step DC voltages as well as base rotation excitation. The electrostatically actuated and detected microgyroscopes are subjected to coupled flexural-flexural vibrations that are related by base rotation. In order to detune the stiffness and natural frequencies of the system, DC voltages are applied to the proof mass electrodes in drive and sense directions. Nonlinear integro differential equations of the system are derived using extended Hamilton principle considering nonlinearities in curvature, inertia, damping and electrostatic forces. Afterward, the Gelerkin decomposition method is implemented to reduce partial differential equations of microgyroscope deflection to a system of nonlinear ordinary equations. By using the 4th order Runge–Kutta method, the nonlinear ordinary equations are solved for various values of damping coefficients, air pressures, base rotation and various initial gaps between the proof mass electrodes and the substrates. Results show that the geometric nonlinearity increases the dynamic pull-in voltage and also consideration of the base rotation gives an improved evaluation of the dynamic instability. It is shown that the squeeze film damping has a considerable influence on the dynamic deflection of the microgyroscopes.


2013 ◽  
Vol 811 ◽  
pp. 474-477
Author(s):  
Chin Chia Liu

Using traditional methods such as perturbation theory or Galerkin approach method to analyze the dynamic response of electrostatic devices is not easy due to the complexity of the interactions between the electrostatic coupling effect, the fringing field effect, the residual stress, the nonlinear electrostatic force and squeeze-film damping effect. Accordingly, the present study proposes a new approach for analyzing the dynamic response of such devices using a hybrid numerical scheme comprising the differential transformation method and the finite difference method by pure DC or combined DC / AC loading. The validity of the proposed scheme is confirmed by comparing the results obtained for the pull-in voltage of the micro-beam with those presented in the literature derived using a variety of schemes. Overall, the results show that the hybrid numerical scheme provides a suitable means of analyzing the nonlinear dynamic behavior of a wide variety of common electrostatically-actuated microstructures.


Author(s):  
Mohammad I. Younis ◽  
Ali H. Nayfeh

A model for the dynamics of electrostatically actuated microplates undergoing large deflections under the effect of squeeze-film damping is presented. The model predicts the quality factors of microplates under a wide range of gas pressures and applied electrostatic forces up to the pull-in instability. The model utilizes the nonlinear Euler-Bernoulli beam equation, the von Ka´rma´n plate equations, and the compressible Reynolds equation. The static deflection of the microplate is calculated using the beam model. Analytical expressions are derived for the pressure distribution in terms of the plate mode shapes around the deflected position using perturbation techniques. The static deflection and the analytical expressions are substituted into the plate equations, which are solved using a finite-element method. Several results are presented showing the effect of the pressure and the electrostatic force on the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors.


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