Squeeze-Film Damping of Flexible Microcantilevers at Low Ambient Pressures

2008 ◽  
Author(s):  
Jin Woo Lee ◽  
Arvind Raman ◽  
Hartono Sumali
Keyword(s):  
Natural Frequencies ◽  
Ambient Pressure ◽  
Slip Boundary Condition ◽  
Squeeze Film ◽  
Continuum Models ◽  
Inertia Effect ◽  
Quality Factors ◽  
Slip Boundary ◽  
Squeeze Film Damping ◽  
Oscillating Plate

An improved theoretical approach is presented to calculate and predict the quality factors of flexible microcantilevers affected by squeeze-film damping at low ambient pressures, and moderate to high Knudsen numbers. Veijola’s model [1], originally derived for a rigid oscillating plate near a wall, is extended to a flexible cantilever beam and both the gas inertia effect and slip boundary condition are considered in deriving resulting damping pressure. The model is used to predict the natural frequencies and quality factors of silicon microcantilevers with small gaps and their dependence on ambient pressure. In contrast to non-slip, continuum models, we find that quality factor depends strongly on ambient pressure, and that the damping of higher modes is more sensitive to ambient pressure than the fundamental.

Squeeze Film Damping Models Compared With Tests on Microsystems

2006 ◽  
Author(s):  
Hartono (Anton) Sumali ◽  
David S. Epp
Keyword(s):  
Experimental Data ◽  
Damping Ratio ◽  
Laser Doppler Vibrometer ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Squeeze Film Damping ◽  
Wide Range ◽  
Oscillation Frequencies ◽  
Oscillating Plate ◽  
The Continuum

This paper compares three models for computing forces caused by gas film squeezed between parallel plates. The models are used to calculate damping forces on an oscillating plate at different oscillation frequencies. The damping forces are then used to calculate nondimensional damping ratios. The damping ratios are used in making comparisons among the models and with experimental data. The experiment used an oscillating MEMS plate suspended by folded springs. The substrate (base) was shaken with a piezoelectric transducer. The plate vibrated as a result, especially at the resonant frequency. The velocities of the suspended plate and of the substrate were measured with a laser Doppler vibrometer and a microscope. Experimental modal analysis gave the damping ratio. To achieve a wide range of squeeze numbers, the experiment was repeated under several different pressures. The measurement was also repeated on an array of plates. Experimental data indicate that, for atmospheric and higher pressures, squeeze-film damping forces can be modeled accurately with a very simple model. For lower pressures in the continuum regime, a more complete model by Veijola (2004) predicts the damping ratio very well.

Dynamic Response of a Piezoelectric Flextensional Microactuator

2005 ◽  
Author(s):  
Jongpil Cheong ◽  
Srinivas Tadigadapa ◽  
Christopher D. Rahn
Keyword(s):  
Dynamic Response ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Rf Mems ◽  
Squeeze Film ◽  
Beam Shape ◽  
Initial Beam ◽  
Carbon Tape ◽  
Squeeze Film Damping ◽  
Soft Carbon

Microactuators capable of providing high resolution displacement and controlled force have many applications in RF MEMS, microfluidics, and motion control. This paper theoretically and experimentally investigates the dynamic response of a piezoelectric flextensional microactuator consisting of a clamped beam that buckles in response to contraction of a bonded PZT support. The DRIE and solder bonding fabrication process produces beams with initial curvature that affects their dynamic response. Unlike previous research where sinusoidal initial beam shapes are analyzed, polynomial initial beam shape enables more accurate prediction of beam natural frequencies and frequency response when compared with experimental results. The inclusion of squeeze film damping between the beam and PZT support enables the model to predict frequency response. Experiments show that mounting the PZT with soft carbon tape limits PZT vibration.

Nonlinear Vibration Analysis of a Dielectric Elastomer Based Microbeam Resonator

2016 ◽  
Vol 846 ◽  
pp. 188-192 ◽  
Author(s):  
Chuang Feng ◽  
Jie Yang ◽  
Liao Liang Ke
Keyword(s):  
Resonant Frequency ◽  
Dynamic Characteristics ◽  
Vibration Analysis ◽  
Vibration Amplitude ◽  
Ambient Pressure ◽  
Dielectric Elastomer ◽  
Squeeze Film ◽  
Beam Resonator ◽  
Squeeze Film Damping ◽  
Electrical Voltage

Dynamic characteristics of a dielectric elastomer based micro beam resonator are investigated by taking into consideration of squeeze-film damping, large deformation and electrical voltage. The analysis shows that the resonant frequency of the resonator can be tuned through changing applied electrical voltage. It is observed that the natural frequency of the resonator increases with the increase of the vibration amplitude. In addition, the ambient pressure can significantly alter the resonant frequency of the resonator. The analysis is envisaged to provide qualitative predictions and guidelines for design and application of DE-based micro resonators.

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 PULL-IN INSTABILITY AND VIBRATION ANALYSIS OF A NONLINEAR MICROCANTILEVER GYROSCOPE UNDER STEP VOLTAGE CONSIDERING SQUEEZE FILM DAMPING

2013 ◽  
Vol 05 (03) ◽  
pp. 1350032 ◽  
Author(s):  
M. MOJAHEDI ◽  
M. T. AHMADIAN ◽  
K. FIROOZBAKHSH
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Proof Mass ◽  
Dynamic Instability ◽  
Squeeze Film ◽  
Electrostatically Actuated ◽  
Damping Coefficients ◽  
Step Voltage ◽  
Runge Kutta Method ◽  
Squeeze Film Damping

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.

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.

Modeling Squeeze-Film Damping of Electrostatically Actuated Microplates Undergoing Large Deflections

2005 ◽  
Author(s):  
Mohammad I. Younis ◽  
Ali H. Nayfeh
Keyword(s):  
Mode Shapes ◽  
Squeeze Film ◽  
Beam Equation ◽  
Large Deflections ◽  
Static Deflection ◽  
Quality Factors ◽  
Electrostatically Actuated ◽  
Squeeze Film Damping ◽  
Plate Equations ◽  
Analytical Expressions

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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