Parametric Excitation of Flexural Vibrations of Micro Beams by Fringing Electrostatic Fields

2010 ◽  
Author(s):  
Slava Krylov ◽  
Nicola Molinazzi ◽  
Tsvi Shmilovich ◽  
Uri Pomerantz ◽  
Stella Lulinsky
Keyword(s):  
Electric Fields ◽  
Parametric Excitation ◽  
Electrostatic Force ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Ambient Air ◽  
Silicon On Insulator ◽  
Suggested Approach ◽  
Base Functions ◽  
Fringing Fields

We report on an approach for efficient excitation of large amplitude flexural out-of-plane vibrations of micro beams and present results of theoretical and experimental feasibility study of the suggested principle. An actuating electrode is located symmetrically at the two sides of the beam and is fabricated from the same layer of the wafer. The electrostatic force is engendered by the asymmetry of the fringing fields in the deformed state and acts in the direction opposite to the deflection therefore increasing the effective stiffness of the system. The time-varying voltage applied to the electrode results in the modulation of this electrostatic stiffness and consequently in the parametric excitation of the structure. The device may exhibit large vibrational amplitudes not limited by the pull-in instability common in close-gap actuators. In contrast to previously reported devices excited by the fringing fields, the force considered here is of distributed character. The reduced order model was built using the Galerkin decomposition with linear modes as base functions and the resulting system of nonlinear differential equations was solved numerically. The electrostatic forces were approximated by means of fitting the results of three-dimensional numerical solution for the electric fields. The devices fabricated from a silicon on insulator (SOI) substrate using deep reactive ion etching (DRIE) based process were operated in ambient air conditions and the responses were registered by means of Laser Doppler Vibrometry. The experimental resonant curves were consistent with those predicted by the model. Theoretical and preliminary experimental results illustrated the feasibility of the suggested approach.

Large Angle Parametrically Excited Tilting Micro Actuator

2008 ◽  
Author(s):  
Assaf Ya’akobovitz ◽  
Slava Krylov
Keyword(s):  
Parametric Excitation ◽  
Inertial Sensors ◽  
Actuation Voltage ◽  
Large Angle ◽  
Three Dimensional ◽  
Single Layer ◽  
Silicon On Insulator ◽  
Performance Study ◽  
Operational Parameters ◽  
Lumped Model

We present novel operational principle of a tilting MEMS device based on parametric excitation and linear to angular motion transformation. The device is fabricated using a single layer of silicon on insulator (SOI) wafer and combines simple fabrication process with several beneficial features including large tilting angles, wide bandwidth, low sensitivity to deviation in geometrical and operational parameters and low actuation voltage. A theoretical feasibility and performance study was carried out using a lumped model of the device and verified by a coupled three-dimensional simulation. Parametric excitation of the tilting motion was demonstrated experimentally using and external piezoelectric transducer and tilting angles of 39° were registered. The suggested operational approach could be efficiently implemented in many MEMS based applications incorporating tilting elements including micromirrors, bio medical devices and inertial sensors.

Collective Dynamics of Arrays of Micro Cantilevers Interacting Through Fringing Electrostatic Fields

2014 ◽  
Author(s):  
Slava Krylov ◽  
Stella Lulinsky ◽  
Bojan R. Ilic ◽  
Inbar Schneider
Keyword(s):  
Dynamic Properties ◽  
Electrostatic Force ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Silicon On Insulator ◽  
Element Analysis ◽  
Mechanical Coupling ◽  
Electrostatic Fields ◽  
Voltage Dependent ◽  
Electrostatic Coupling

We investigate the collective nonlinear behavior of an array of micro cantilevers interacting by fringing electrostatic fields and fabricated of silicon on insulator (SOI) wafer. The interaction is due to the mechanical coupling originated in the flexibility of the anchor and of the electrostatic coupling through voltage-dependent electrostatic force. In the framework of the reduced order model based on the Galerkin decomposition the array is considered as an assembly of single degree of freedom oscillators. The mechanical coupling matrix is extracted using the full scale finite element analysis of the array while the electrostatic force is approximated by a fit build using the three-dimensional numerical simulation. We show numerically and experimentally that large amplitude collective vibrations of the array can be achieved using parametric excitation while the dynamic properties of the array can be efficiently tuned by the applied voltage.

Structural Behavior of Microbeams Actuated by Out-of-Plane Electrostatic Fringing-Fields

2013 ◽  
Author(s):  
Hassen M. Ouakad
Keyword(s):  
Electrostatic Force ◽  
Order Model ◽  
Electrostatic Problem ◽  
Reduced Order ◽  
Gate Electrodes ◽  
Out Of Plane ◽  
Base Functions ◽  
Mems Device ◽  
System Frequency ◽  
Fringing Fields

In this paper, we present an investigation of the static behavior of a doubly-clamped microbeam actuated electrically through out-of-plane electrostatic fringing-fields. The distributed electrostatic force is caused by the asymmetry of the fringing-fields. This is actually due to the out-of-plane asymmetry of the beam and its two actuating stationary electrodes. The electric force was approximated by means of fitting the results of two-dimensional numerical solution of the electrostatic problem using Finite-Element Method (FEM). Then, a reduced-order model (ROM) was built using the Galerkin decomposition with linear undamped modes of a clamped-clamped beam as base functions. The ROM equations are solved numerically to get the static response of the considered micro-actuator when actuated by a DC load. Results shows possibility of having three different regimes for this particular MEMS device: a bending regime, a catenary regime, and an elastic regime. Eigenvalue problem is then solved to get the variation of the fundamental natural frequency when the system is deflected by a DC load. Results show that controlling the microbeam stroke, with a DC voltage on the gate electrodes, enables us to tune the system frequency, resulting in a possibility of a tunable MEMS device without a pull-in scenario.

Bistable Threshold Sensor With Mechanically Nonlinear Self-Limiting Suspension and Electrostatic Actuation

2011 ◽  
Author(s):  
Shila Rabanim ◽  
Emil Amir ◽  
Slava Krylov
Keyword(s):  
Dynamic Range ◽  
Electrostatic Force ◽  
Silicon On Insulator ◽  
Stable Configuration ◽  
Curved Beams ◽  
Suggested Approach ◽  
Deep Reactive Ion Etching ◽  
Electrostatically Actuated ◽  
Contact Devices

We report on the operational principle, modeling, fabrication and characterization of an electrostatically actuated force/acceleration sensor with mechanically nonlinear stiffening suspension. The suspension incorporates initially curved beams oriented in such a way that both the electrostatic and inertial forces applied to the beam’s ends are directed predominantly along the beam. Since the stiffness of the curved beam is significantly lower than that of the straightened beam, the force-displacement dependence of the suspension is of the self-limiting type while the suspension itself serves as a compliant constraint. Application of a softening electrostatic force, provided by a parallel-plate transducer, results in pull-in instability followed by the steep increase in the suspension stifftness and the appearance of an additional stable configuration of the device. In accordance with the model results the dependence between the acceleration and the shift of the pull-in voltage induced by the acceleration is nearly linear and the pull-in voltage monitoring can be used for the measurement of the acceleration. Model results show that using the suggested approach significantly improves device resolution, extends dynamic range, and improves reliability by eliminating contact. Devices of several configurations were fabricated from a silicon on insulator (SOI) substrate using a deep reactive ion etching (DRIE) based process. Preliminary experimental results imply that the suggested approach is feasible.

scholarly journals Fully three-dimensional analysis of a photonic crystal assisted silicon on insulator waveguide bend

2018 ◽  
Vol 32 (31) ◽  
pp. 1850344 ◽  
Author(s):  
N. Eti ◽  
Z. Çetin ◽  
H. S. Sözüer
Keyword(s):  
Photonic Crystal ◽  
Numerical Study ◽  
Fdtd Method ◽  
Three Dimensional ◽  
Silicon On Insulator ◽  
Geometrical Parameters ◽  
Low Loss ◽  
Bending Loss ◽  
Difference Time ◽  
Waveguide Bend

A detailed numerical study of low-loss silicon on insulator (SOI) waveguide bend is presented using the fully three-dimensional (3D) finite-difference time-domain (FDTD) method. The geometrical parameters are optimized to minimize the bending loss over a range of frequencies. Transmission results for the conventional single bend and photonic crystal assisted SOI waveguide bend are compared. Calculations are performed for the transmission values of TE-like modes where the electric field is strongly transverse to the direction of propagation. The best obtained transmission is over 95% for TE-like modes.

Numerical modelling of twisted nematic devices

1983 ◽  
Vol 309 (1507) ◽  
pp. 203-216 ◽  
Keyword(s):  
Liquid Crystal ◽  
Electric Fields ◽  
Low Cost ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Crystal Layer ◽  
Liquid Crystal Layer ◽  
Chiral Nematic ◽  
Twisted Nematic ◽  
Three Dimensional Simulations

Over most of each active region in nematic and chiral nematic twist cells the motion and configuration of the liquid crystal layer does not vary appreciably with position parallel to the surfaces. In such laminar regions the statics, dynamics and optics ot the cell can be accurately simulated at low cost on a computer of moderate size, given the appropriate physical parameters. Methods and recent advances in simulation of laminar regions are reviewed. Bistable twist cells are simulated for illustration. Important problems of stability and edge effects in the presence of electric fields await solution with two- or three-dimensional simulations.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

Three-Dimensional Simulation for Perikinetic Flocculation of Fine Sediment under the Ionization in Still Water

2011 ◽  
Vol 356-360 ◽  
pp. 2282-2290
Author(s):  
Lin Shuang Liu ◽  
Xin Luo ◽  
Guo Lu Yang ◽  
Ming Hui Yu
Keyword(s):  
Electrostatic Force ◽  
Three Dimensional ◽  
Fine Sediment ◽  
Radius Of Gyration ◽  
Brownian Dynamic ◽  
System A ◽  
Simulation Based ◽  
Dimensional Simulation ◽  
Original Cell ◽  
Random Variation

A simulation based on Brownian dynamic for perikinetic flocculation of fine sediment under the ionization is presented. The Langevin equation is used as dynamical equation for tracking each particle making up a floc. Monte Carlo method was used for simulate random variation in particle movement. An initial condition and periodic boundary condition which conformed to reality well is used for calculation. In each cell 1000 particles of 10𝝁 m, 15𝝁m, 20𝝁m, 25𝝁m, 30𝝁m in diameter were served as primary particles. Floc growth is based on the thermal force and the electrostatic force. The electrostatic force on a particle in the simulation cell is considered as a sum of the electrostatic force from other particles in the original cell. The particles are supposed to be motion with uncharged and charged state in dispersion system. A comparison of the initial flocculent time and smashing time in sludge density 1010kg/m3, 1025 kg/m3, 1050 kg/m3, 1075 kg/m3, 1100 kg/m3were present to show the effect of it on floc growth. The increase of sludge density deferred the flocculation rate. To study morphological shape of floc, the radius of gyration was revealed under different situations. On one hand the radius of gyration presented random variation with uncharged particle, On the other hand, the radius of gyration increases gradually with the increase of polar electrical charges on primal particle. Moreover, the morphological shape for the charged floc was more open than that of unchanged state. Finally, a series of experimental results are present, which is coincide with model well.

Numerical Simulation of the Flow and Heat Transfer Induced by Corona Discharge Coupling with Electrostatically Forced Vibration

2021 ◽  
Author(s):  
Yeng-Yung Tsui ◽  
Hao-Yu Lin ◽  
Ting-Kai Wei ◽  
Yu-Jie Huang ◽  
Chi-Chuan Wang
Keyword(s):  
Heat Transfer ◽  
Corona Discharge ◽  
Electrostatic Force ◽  
Three Dimensional ◽  
Resonant Mode ◽  
Finite Volume Methods ◽  
Flexible Plate ◽  
Ionic Wind ◽  
Plate Electrode ◽  
Oscillatory Movement

Abstract A thin, flexible plate electrode was adopted to generate both ionic wind and vibration in our previous study. The design contains a metal inductor placed next to the plate electrode so that it is attracted to vibrate by the induced electrostatic force. The resulting flow was used to enhance heat transfer. In this study, a numerical methodology is developed to unveil the flow structure induced by the corona discharge and electrode vibration. The oscillatory movement of the electrode is modeled as a cantilever beam vibrating at its first resonant mode. The electric and flow fields are solved by the finite volume methods. It is shown that a jet-like flow is generated by the electric discharge. The oscillatory movement of the jet results in flat temperature profile in comparison with the corona only system. Owing to the unsteady characteristic, the jet strength is less strong than that without vibration. The calculated results are qualitatively in line with the experiments, though some considerable differences exist. It is found that the oscillatory flow brings about lower overall heat transfer effectiveness than that without vibration regardless of the corona voltage. On the contrary, experiments showed that heat transfer is enhanced at low corona voltages where the ionic wind is not so overwhelming. The disagreement is mainly attributed to the 2-D assumption made in the simulation. The experimental arrangement, the corona discharge, and the vortex flows resulted all are three-dimensional. Therefore, 3-D calculations become necessary.

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