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

Reduced Order Model ◽

Circular Plates ◽

Order Model ◽

Reduced Order ◽

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.

Volume 2: Modeling and Control of Engine and Aftertreatment Systems; Modeling and Control of IC Engines and Aftertreatment Systems; Modeling and Validation; Motion Planning and Tracking Control; Multi-Agent and Networked Systems; Renewable and Smart Energy Systems; Thermal Energy Systems; Uncertain Systems and Robustness; Unmanned Ground and Aerial Vehicles; Vehicle Dynamics and Stability; Vibrations: Modeling, Analysis, and Control ◽

Voltage Response of Parametric Resonance of MEMS Circular Plates Under Hard Excitations

10.1115/dscc2019-9059 ◽

2019 ◽

Author(s):

Julio S. Beatriz ◽

Dumitru I. Caruntu

Keyword(s):

Parametric Resonance ◽

Multiple Scales ◽

Electrostatic Force ◽

Voltage Response ◽

Circular Plates ◽

Order Model ◽

Reduced Order ◽

Modes Of Vibration

Abstract This work deals with the voltage response of parametric resonance of electrostatically actuated microelectromechanical (MEMS) circular plates under hard excitations. Method of Multiple Scales (MMS) and Reduced Order Model (ROM) method using two modes of vibration are used to predict the voltage-amplitude response of the MEMS circular plates. ROM is solved using AUTO 07p, a software package for continuation and bifurcation. MMS used in this paper has one term in the electrostatic force being considered significant. This is the way MMS is used to model hard excitations. MMS shows results similar to those of ROM at lower amplitudes and lower voltages. The differences between the two methods, MMS and ROM, are significant in high amplitudes for all voltages, and the differences are significant in all amplitudes for larger voltages. Significant differences can be noted in the effect of different parameters such as the detuning frequency and damping on the voltage response. ROM AUTO 07p is calibrated using ROM time responses in which the ROM is solved using the solver ode15s in Matlab.

Reduced Order Model of Electrostatically Actuated MEMS Resonators Resonance Near Half Natural Frequency

Volume 1: 24th Conference on Mechanical Vibration and Noise, Parts A and B ◽

10.1115/detc2012-70326 ◽

2012 ◽

Author(s):

Dumitru I. Caruntu ◽

Israel Martinez ◽

Martin W. Knecht

Keyword(s):

Frequency Response ◽

Natural Frequency ◽

Multiple Scales ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Amplitude Frequency Response ◽

Mems Resonators

This paper uses the Reduced Order Model (ROM) method to investigate the influence of nonlinearities from parametric electrostatic excitation due to soft AC voltage of frequency near half natural frequency of the MEMS cantilever resonator on its frequency response. Most of the analysis in literature investigates pull-in phenomenon, stability, amplitude–frequency relations, or finds time responses of such systems. In this work it is showed that the bifurcation points in the amplitude-frequency response occur at lower frequencies and amplitudes than predicted by the Method of Multiple Scales (MMS), a perturbation method. This result is extremely important for predicting pull-in phenomena. Also the ROM predicts pull-in instability for large initial amplitudes and AC frequencies less than half natural frequency of the resonator. MMS fails to predict this behavior. Increasing the damping and/or decreasing the voltage increases the frequency at which the system undergoes into a pull-in phenomenon.

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

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-85963 ◽

2012 ◽

Author(s):

Dumitru I. Caruntu ◽

Israel Martinez

Keyword(s):

Natural Frequency ◽

Nonlinear Response ◽

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).

Volume 2: Control, Monitoring, and Energy Harvesting of Vibratory Systems; Cooperative and Networked Control; Delay Systems; Dynamical Modeling and Diagnostics in Biomedical Systems; Estimation and Id of Energy Systems; Fault Detection; Flow and Thermal Systems; Haptics and Hand Motion; Human Assistive Systems and Wearable Robots; Instrumentation and Characterization in Bio-Systems; Intelligent Transportation Systems; Linear Systems and Robust Control; Marine Vehicles; Nonholonomic Systems ◽

Reduced Order Model of Parametric Resonance of Electrostatically Actuated CNT Cantilever Resonators

10.1115/dscc2013-3922 ◽

2013 ◽

Author(s):

Dumitru I. Caruntu ◽

Le Luo

Keyword(s):

Parametric Resonance ◽

Multiple Scales ◽

Van Der Waals ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Carbon Nano Tubes ◽

Ground Plate ◽

Phase Behaviors

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model (ROM) method. Forces acting on the CNT cantilever are electrostatic, van der Waals, and damping. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS), and ROM are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behaviors are found in the case of parametric resonance.

Volume 6: ASME Power Transmission and Gearing Conference; 3rd International Conference on Micro- and Nanosystems; 11th International Conference on Advanced Vehicle and Tire Technologies ◽

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

10.1115/detc2009-87024 ◽

2009 ◽

Cited By ~ 6

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 ◽

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

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4023164 ◽

2012 ◽

Vol 8 (3) ◽

Cited By ~ 23

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 ◽

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.

Volume 1: Advances in Control Design Methods, Nonlinear and Optimal Control, Robotics, and Wind Energy Systems; Aerospace Applications; Assistive and Rehabilitation Robotics; Assistive Robotics; Battery and Oil and Gas Systems; Bioengineering Applications; Biomedical and Neural Systems Modeling, Diagnostics and Healthcare; Control and Monitoring of Vibratory Systems; Diagnostics and Detection; Energy Harvesting; Estimation and Identification; Fuel Cells/Energy Storage; Intelligent Transportation ◽

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

10.1115/dscc2016-9714 ◽

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 ◽

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.

Reduced Order Model of Two Coupled MEMS Parallel Cantilever Resonators Under DC and AC Voltage Near Natural Frequency

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-85966 ◽

2012 ◽

Author(s):

Dumitru I. Caruntu ◽

Kyle N. Taylor

Keyword(s):

Frequency Response ◽

Natural Frequency ◽

Multiple Scales ◽

Equations Of Motion ◽

Reduced Order Model ◽

Lagrange Equations ◽

Order Model ◽

Reduced Order ◽

Dc Voltage ◽

Ground Plate

This paper deals with a system of two coupled parallel identical MEMS cantilever resonators and a ground plate. Alternating Current (AC) and Direct Current (DC) voltages are applied between the first resonator and ground plate, and a DC voltage applied between the resonators. The AC voltage frequency is near natural frequency of the resonators. The electrostatic forces produced by voltages are nonlinear. System equations of motion are obtained using Lagrange equations, then nondimensionalized. The Method of Multiple Scales (MMS) is used to find the steady state frequency response. The Reduced Order Model (ROM) is used to validate MMS results. Matlab is used to find cantilever frequency response of the resonator tip. The DC voltage between resonators is showed to significantly influence the response of the first resonator.