Dynamic Trapping in Bi-Stable Electrostatically Actuated Curved Micro Beams

2014 ◽  
Author(s):  
Lior Medina ◽  
Rivka Gilat ◽  
Slava Krylov
Keyword(s):  
Stable State ◽  
Stable Configuration ◽  
Structural Elements ◽  
Dynamic Phenomenon ◽  
Order Model ◽  
Reduced Order ◽  
Actuation Force ◽  
Numerical Investigations ◽  
Electrostatically Actuated ◽  
Beam Characteristics

Micro and nano devices incorporating bi-stable structural elements such as micro beams are designed to exploit the fact that the latter possess two stable configurations at the same actuation force. Generally, the transition of a micro beam from one table state to another, namely the snap-through which is essentially dynamic phenomenon, can be initiated by either static or dynamic activations. In this work, results of theoretical and numerical investigations of the transient dynamics of a pre-stressed initially curved double clamped micro beams actuated by a time dependent electrostatic load are presented. We show by means of a reduced order model of a shallow beam, derived using the Galerkin procedure, that the beam may exhibit various types of responses. For certain beam characteristics, the second stable state is inaccessible under a static loading but is attainable only by means of a specially tailored dynamic actuation. This gives way to the possibility of trapping the dynamically bi-stable beam at a stable configuration which is close to the electrode by applying special loading sequences.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for uniform microresonators with mass deposition and without are reported.

ROM of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Second Order ◽  
Voltage Response ◽  
Order Model ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Method Effects ◽  
Ground Plate

This paper deals with the voltage-amplitude response (or voltage response) of superharmonic resonance of second order of MEMS resonator sensors under electrostatic actuation. The system consists of a MEMS flexible cantilever above a parallel ground plate. The AC frequency of actuation is near one fourth the natural frequency. The voltage response of the superharmonic resonance of second order of the structure is investigated using the Reduced Order Model (ROM) method. Effects of voltage and damping voltage response are reported.

Voltage Response of Superharmonic Resonance of Electrostatically Actuated MEMS Resonators: Comparison Between Boundary Value Problem Model and Reduced Order Model

2018 ◽  
Author(s):  
Julio Beatriz ◽  
Martin Botello ◽  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value ◽  
Mode Shapes ◽  
Voltage Response ◽  
Order Model ◽  
Partial Differential ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Modes Of Vibration

This paper deals with the voltage response of electrostatically actuated NEMS resonators at superharmonic resonance. In this work a comparison between Boundary Value Problem (BVP) model, and Reduced Order Model (ROM) is conducted for this type of resonance. BVP model is developed from the partial differential equation by replacing the time derivatives with finite differences. So, the partial differential equation is replaced by a sequence of boundary value problems, one for each step in time. Matlab’s function bvp4c is used to numerically integrate the BVPs. ROMs are based on Galerkin procedure and use the mode shapes of the resonator as a basis of functions. Therefore, the partial differential equation is replaced by a system of differential equations in time. The number of the equations in the system is equal to the number of mode shapes (or modes of vibration) used in the ROM. One mode of vibration ROM is solved using the method of multiple scales. Two modes of vibration ROM is numerically integrated using Matlab’s function ode15s in order to obtain time responses, and a continuation and bifurcation analysis is conducted using AUTO 07P. The effects of different nonlinearities in the system on the voltage response are reported. This work shows that BVP model is a valid method to predict the voltage response of a micro/nano cantilevers.

Frequency Response of Parametric Resonance of Electrostatically Actuated Circular Plates Under Hard Excitations

2019 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Frequency Response ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Reduced Order Model ◽  
Circular Plates ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Modes Of Vibration

Abstract In this paper, the Method of Multiple Scales, and the Reduced Order Model method of two modes of vibration are used to investigate the amplitude-frequency response of parametric resonance of electrostatically actuated circular plates under hard excitations. Results show that the Method of Multiple Scales is accurate for low voltages. However, it starts to separate from the Reduced Order Model results as the voltage values are larger. The Method of Multiple Scales is good for low amplitudes and weak non-linearities. Furthermore the Reduced Order Model running with AUTO 07p is validated and calibrated using the 2 Term ROM time responses.

Reduced Order Model for MEMS Cantilever Resonators Under Soft AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator is investigated. The AC voltage is of frequency near resonator’s natural frequency. A first order fringe correction of the electrostatic force and viscous damping are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for the uniform microresonator are compared with those obtained via the Method of Multiple Scales (MMS).

Nonlinear Dynamics of MEMS Arches

2010 ◽  
Author(s):  
Sami Alkharabsheh ◽  
Mohammad Younis
Keyword(s):  
Electrostatic Force ◽  
Equations Of Motion ◽  
Amplitude Dependence ◽  
Harmonic Load ◽  
Order Model ◽  
Shooting Technique ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Dynamic Phenomena ◽  
Unstable States

In this paper, the dynamic response of electrostatically actuated clamped-clamped arch microbeam is investigated when excited by a DC load superimposed to an AC harmonic load. The dynamic analysis is carried out using a Galerkin-based reduced order model along with a shooting technique to find periodic motions and analyzing its stability using a Floquet theory. Results are presented for the cases of primary and super harmonic resonances. We found several nonlinear dynamic phenomena due to the inherent nonlinear electrostatic force and geometric nonlinearity of the arch. These include frequency-amplitude dependence, jumps, tangent bifurcations, coexistence of solutions, and softening and hardening behaviors. The shooting technique showed high robustness in capturing both the stable and unstable states of the system. Hence, it helped clarify vague behaviors that were previously reported using longtime integration of the equations of motion.

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Alternating Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Fringe Effect

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

Reduced Order Model on DC Bias Effect on the Frequency Response of Electrostatically Actuated Biosensor Microplates

2016 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Electrostatic Force ◽  
Alternate Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Bias Effect ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Ground Plate ◽  
Dc Bias

This paper investigates the frequency response of microplates under electrostatic actuation. The microplate is parallel to a fixed ground plate. The electrostatic force that actuates the system is given by both Alternate Current (AC) and Direct Current (DC) voltages. The AC frequency is set to be near half natural frequency of the structure. Damping influence is also investigated in this paper. The method of investigation is Reduced Order Model. The effects of various parameters on the response of the structure are reported.

Model Reduction for the Electrostatically Actuated Silicon Diaphragm Based on Modal-Type Dynamic Condensation

2014 ◽  
Author(s):  
X. Z. Lin ◽  
Z. M. Hu ◽  
J. M. Huang
Keyword(s):  
Dynamic Models ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Stiffness Matrices ◽  
Electric Driving ◽  
Dynamic Condensation ◽  
Simulation Results ◽  
Modal Type

A method for constructing reduced-order models (ROM) of an electrostatically actuated clamped silicon diaphragm is presented. This reduced-order model is constructed by using basis the spatially dependent eigen-functions. A commercial finite element package is firstly used to form the system mass and stiffness matrices representing the model. These matrices are then manipulated in MATLAB™ and reduced using modal type dynamic condensation. The eigen-value problem is then solved for the reduced mass and stiffness matrices and subset of the modes are used to producing low-order but highly accurate models of electrostatically actuated diaphragm. The reduced-order model can accounts for general residual stress and strain hardening and allows for any other electric driving signal simulations. Once the ROM has been generated, it can be reused to simulate the quasi-state and dynamics behaviors of the device over a range of different electric driving waveforms. The calculated results show that the resulting ROM can capture the static/dynamic behaviors of the device very well. The simulation results also show good agreement with the fully meshed dynamic models simulation results, thus the efficiency and accuracy of the modeling technology are valid.

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