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.

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.

The Effect of Squeeze-Film Damping on Suppressing the Shock Response of MEMS

2009 ◽  
Author(s):  
Hadi Yagubizade ◽  
Mohammad I. Younis ◽  
Ghader Rezazadeh
Keyword(s):  
Reynolds Equation ◽  
Element Model ◽  
Squeeze Film ◽  
Beam Equation ◽  
Mechanical Shock ◽  
Shock Loads ◽  
Reduced Order ◽  
Squeeze Film Damping ◽  
Nonlinear Finite Element Model ◽  
Euler Bernoulli Beam

This paper presents an investigation into the response of a clamped-clamped microbeam to mechanical shock under the effect of squeeze-film damping (SQFD). In this work, we solve simultaneously the nonlinear Reynolds equation, to model squeeze-film damping, coupled with a nonlinear Euler-Bernoulli beam equation. A Galerkin-based reduced-order model and a finite-deference method (FDM) are utilized for the solid domain and for the fluid domain, respectively. Several results showing the effect of gas pressure on the response of the microbeams are shown. Comparison with the results of a multi-physics nonlinear finite-element model is presented. The results indicate that squeeze-film damping has more significant effect on the response of microstructures in the dynamic shock loads compared to the quasi-static shock loads.

Modeling of Kinetic to Electrical Energy Conversion via Capacitive MEMS With Switchable Dielectric

2008 ◽  
Author(s):  
Asantha Kempitiya ◽  
Mona M. Hella ◽  
Diana A. Borca-Tasciuc
Keyword(s):  
Dielectric Constant ◽  
Electrostatic Force ◽  
Electrical Energy ◽  
Dielectric Medium ◽  
Squeeze Film ◽  
Quality Factors ◽  
Electric Power Supply ◽  
Biomedical Monitoring ◽  
Micro Sensor ◽  
High Dielectric

Wireless distributed micro-sensor systems have numerous applications, from equipment diagnostic and control to real time biomedical monitoring. A major obstacle in developing autonomous micro-sensor networks is the need for local, autonomous electric power supply, since using a battery is often not a viable solution. This work investigates a novel micro-power generator converting ambient vibrations to electrical energy via electrostatic transduction employing a comb-like variable capacitor, with a switchable dielectric constant. The micro-generator is designed to operate in an inplane, gap closing, and charge constrained configuration. Enhanced power levels are obtained by pulling a high dielectric constant liquid between the capacitor gaps via electrochemical force effect at maximum capacitance position. The effects of squeeze film damping and variable electrostatic force induced by the varying spatial distribution of dielectric medium are taken into account. In this configuration the microgenerator exhibits high quality factors, thus providing an output power higher of approximately 168 μW.

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.

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.

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.

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.

A Study of Non-Uniform SPST RF-MEMS Switch under the Effect of Squeeze Film Damping

2013 ◽  
Vol 339 ◽  
pp. 157-162
Author(s):  
Omar A. Awad ◽  
Ameen El-Sinawi ◽  
Maher Bakri-Kassem ◽  
Taha Landolsi
Keyword(s):  
Rf Mems ◽  
Mode Shapes ◽  
Squeeze Film ◽  
Rf Mems Switch ◽  
Mems Switch ◽  
Squeeze Film Damping ◽  
Squeeze Film Effect ◽  
Proposed Model ◽  
Modal Model ◽  
Hankel Norm

This work presents a practical technique that can be used to construct the dynamic model of any RF MEMS switch regardless of its shape. The presented technique also allows for inclusion of squeeze film effect in the model without resorting to complex mathematical development of the latter. The technique utilizes Finite element methods to determine mode shapes and natural frequencies of the switch. A modal-model is then constructed from the FEA results. The model can be reduced using by retaining modes with highest Hankel norm modes to reduce calculations effort associated with large models. Simulation results have shown that the proposed model has merit and agrees with published experimental data.

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.

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