An Investigation for the Nonlinear Effects of Squeeze Film Damping and Electrostatic Forces on the Shock Spectrum of a Capacitive Accelerometer

2008 ◽  
Author(s):  
Mahmoud I. Ibrahim ◽  
Mohammad I. Younis
Keyword(s):  
Dynamic Range ◽  
Electrostatic Force ◽  
Nonlinear Effects ◽  
The Other ◽  
Squeeze Film ◽  
Electrostatic Forces ◽  
Single Degree Of Freedom ◽  
Capacitive Accelerometer ◽  
Squeeze Film Damping ◽  
Simulation Results

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.

Damping Analysis of Asymmetrical Comb Accelerometer

2007 ◽  
Vol 353-358 ◽  
pp. 2597-2600 ◽  
Author(s):  
Wei Ping Chen ◽  
Zhen Gang Zhao ◽  
Xiao Wei Liu ◽  
Yu Min Lin
Keyword(s):  
Damping Ratio ◽  
Resonance Phenomenon ◽  
Damping Coefficient ◽  
Anodic Bonding ◽  
Squeeze Film ◽  
Frequency Bandwidth ◽  
Vibration Method ◽  
Capacitive Accelerometer ◽  
Squeeze Film Damping

The resonance phenomenon is suppressed by adjusting the damping of the comb accelerometer structure to widen the frequency bandwidth of the capacitive accelerometer. The capacitive accelerometer with asymmetrical combs, fabricated with DRIE and anodic bonding, is presented. The damping category of the accelerometer is introduced, in which the squeeze-film damping coefficient and the damping ratio factor are detailed. The damping ratio factor of the accelerometer, measured by a vibration method, is 0.17. The damping ratio factor of the optimized structure is calculated of 0.15 to 0.18 with the change of experiential modulus C from 25 to 30, theoretically.

Simulation of Squeeze-Film Damping of Microplates Actuated by Large Electrostatic Load

2007 ◽  
Vol 2 (3) ◽  
pp. 232-241 ◽  
Author(s):  
Mohammad I. Younis ◽  
Ali H. Nayfeh
Keyword(s):  
Electrostatic Force ◽  
Mode Shapes ◽  
Squeeze Film ◽  
Beam Equation ◽  
Beam Model ◽  
Static Deflection ◽  
Quality Factors ◽  
Squeeze Film Damping ◽  
Plate Equations ◽  
Analytical Expressions

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.

Dynamic Analysis of Electrically Actuated Rectangular Microplates With Nonlinear Plate Theory Under Squeeze-Film Damping Effect

2008 ◽  
Author(s):  
S. Ahmad Tajalli ◽  
Mahdi Moghimi Zand ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Plate Theory ◽  
Electrostatic Force ◽  
Equations Of Motion ◽  
Fem Simulation ◽  
Squeeze Film ◽  
Classical Plate Theory ◽  
Singular Value Decomposition Method ◽  
Squeeze Film Damping ◽  
Electrically Actuated ◽  
Value Decomposition

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.

scholarly journals Dynamics of Nonlinear Coupled Electrostatic Micromechanical Resonators under Two-Frequency Parametric and External Excitations

2010 ◽  
Vol 17 (6) ◽  
pp. 759-770 ◽  
Author(s):  
Wen-Ming Zhang ◽  
Guang Meng ◽  
Ke-Xiang Wei
Keyword(s):  
Dynamic System ◽  
Quality Factor ◽  
Electrostatic Force ◽  
Squeeze Film ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Phenomena ◽  
Electrostatically Actuated ◽  
Squeeze Film Damping ◽  
Mems Resonators ◽  
Parametric And External Excitations

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.

Dynamic Analysis of Micro Devices with Squeeze-Film Damping Effect Using Hybrid Numerical Scheme

2013 ◽  
Vol 811 ◽  
pp. 474-477
Author(s):  
Chin Chia Liu
Keyword(s):  
Dynamic Response ◽  
Numerical Scheme ◽  
Coupling Effect ◽  
Electrostatic Force ◽  
Transformation Method ◽  
Squeeze Film ◽  
Damping Effect ◽  
Squeeze Film Damping ◽  
Fringing Field Effect ◽  
Electrostatic Coupling

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.

A Silicon Capacitive Seismic Accelerometer with a Simple Fabrication Process

2011 ◽  
Vol 130-134 ◽  
pp. 4088-4091
Author(s):  
Qing He ◽  
Dong Hai Qiao
Keyword(s):  
Single Crystal ◽  
Sandwich Structure ◽  
Ambient Pressure ◽  
Single Crystal Silicon ◽  
Squeeze Film ◽  
Q Factor ◽  
Crystal Silicon ◽  
Capacitive Accelerometer ◽  
Damping Effect ◽  
Squeeze Film Damping

In this paper, a single-crystal silicon capacitive accelerometer is put forward. The accelerometer is composed of a single-crystal silicon vibration head and two backplates, forming a sandwich structure. With damping holes fabricated on backplates, the squeeze-film damping effect is reduced and a Q factor around 0.7 is obtained. This accelerometer has a simple fabricating process including wet and dry etching and ambient pressure packaging. Its tested sensitivity is 22.6pF/g and calculated noise level is lower than 100ng/√Hz, thus meets the demand of seismic applications.

Fringing Electrostatic Field Actuation of Microplates for Open Air Environment Sensing

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Avinoam Rabinovich ◽  
Assaf Ya'akobovitz ◽  
Slava Krylov
Keyword(s):  
Electrostatic Force ◽  
Fringe Field ◽  
Squeeze Film ◽  
Expansion Theorem ◽  
Electrostatically Actuated ◽  
Squeeze Film Damping ◽  
Element Simulation ◽  
Fringing Field ◽  
Field Lines ◽  
Operational Failure

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.

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