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.

Nonlinear Vibration of Electrostatically Actuated MEMS Resonators Under Parametric and External Excitations

2007 ◽  
Author(s):  
Wen-Ming Zhang ◽  
Guang Meng ◽  
Di Chen
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Squeeze Film ◽  
Electrostatically Actuated ◽  
Squeeze Film Damping ◽  
Mems Resonators ◽  
Nonlinear Dynamic Characteristics ◽  
Dynamical Parameters ◽  
Parametric And External Excitations ◽  
Significant Attention

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.

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.

A Fully Coupled FEM Model of Electromechanically Actuated MEMS With Squeeze Film Damping

2009 ◽  
Author(s):  
Stephan D. A. Hannot ◽  
Daniel J. Rixen
Keyword(s):  
Rf Mems ◽  
Squeeze Film ◽  
Fem Model ◽  
Mems Switch ◽  
Squeeze Film Damping ◽  
Air Damping ◽  
Mems Resonators ◽  
Fluid Damping ◽  
Frequency Behavior ◽  
Damping Model

A specific type of Microsystems or MEMS is the so called RF-MEMS switch. In contrast to MEMS resonators switches generally do not operate in a vacuum. Therefore at the small scales of MEMS fluid (or air) damping is the most dominant damping form. This means that if one is interested in transient or frequency behavior a proper damping model is required. This paper presents a way of using the non-linear Reynolds equation to model the squeeze film damping that is often the type of fluid damping present in these switches. The formulation is provided ready for FEM implementation. Also the tangent matrices required for linearized eigen frequencies are derived. The equations are tested on a model of simple micro switch. The results show that with this model it is possible to predict the damped motion as well as the frequency behavior. The frequency results also show that damping shifts the zero frequency point away from the pull-in point. With a simple mechanical contact model it is also possible to model the closing and opening transient of a microsystem.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document