Casimir Effect on Amplitude-Frequency Response of Parametric Resonance of Electrostatically Actuated NEMS Cantilever Resonators

This paper deals with Casimir and van der Waals effects on the frequency response of parametric resonance of electrostatically actuated NEMS circular plates for bio-sensing applications. The bio-NEMS resonator consists of a clamped circular elastic plate over a fixed electrode plate. A soft AC voltage of frequency near natural frequency between the plates gives an electrostatic force that leads the elastic plate into vibration which leads to parametric resonance that can be used afterwards for biosensing purposes. Frequency response and the effects of Casimir, and van der Waals forces on the response are reported.

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

Volume 8: 31st Conference on Mechanical Vibration and Noise ◽

10.1115/detc2019-98104 ◽

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.

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Bio-MEMS Circular Plate Sensors Under Electrostatic Hard Excitations: Frequency Response of Superharmonic Resonance of Fourth Order

Volume 1: 14th International Conference on Micro- and Nanosystems (MNS) ◽

10.1115/detc2020-22229 ◽

2020 ◽

Author(s):

Julio Beatriz ◽

Dumitru I. Caruntu

Keyword(s):

Frequency Response ◽

Circular Plate ◽

Fourth Order ◽

Multiple Scales ◽

Superharmonic Resonance ◽

Electrostatically Actuated ◽

Amplitude Frequency Response ◽

Elastic Circular Plate ◽

Modes Of Vibration ◽

The Difference

Abstract This paper investigates the frequency-amplitude response of electrostatically actuated Bio-MEMS clamped circular plates under superharmonic resonance of fourth order. The system consists of an elastic circular plate parallel to a ground plate. An AC voltage between the two plates will lead to vibrations of the elastic plate. Method of Multiple Scales, and Reduced Order Model with two modes of vibration are the two methods used in this work. The two methods show similar amplitude-frequency response, with an agreement in the low amplitudes. The difference between the two methods can be seen for larger amplitudes. The effects of voltage and damping on the amplitude-frequency response are reported. The steady-state amplitudes in the resonant zone increase with the increase of voltage and with the decrease of damping.

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On Nonlinear Dynamics of Nanotweezers

Volume 4: 21st Design for Manufacturing and the Life Cycle Conference; 10th International Conference on Micro- and Nanosystems ◽

10.1115/detc2016-60400 ◽

2016 ◽

Author(s):

Dumitru I. Caruntu ◽

Bin Liu

Keyword(s):

Nonlinear Dynamics ◽

Frequency Response ◽

Parametric Resonance ◽

Taylor Series ◽

Multiple Scales ◽

Method Of Multiple Scales ◽

Van Der Waals ◽

Van Der Waals Forces ◽

The Other ◽

Amplitude Frequency Response

This paper deals with amplitude-frequency response of electrostatic nanotube nanotweezer device system. Soft alternating current (AC) of frequency near natural frequency actuates the nanotubes. This leads the system into parametric resonance. The Method of Multiple Scales (MMS) in which the nonlinear electrostatic and van der Waals forces are expanded in Taylor series is used to compare two expansions, one up to third power and the other up to fifth power. The frequency response of the system is reported and the effects of van der Waals forces, electrostatic forces, and damping forces on the frequency response are investigated.

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Comparison of Frequency Response of Parametric Resonance of DWCNT and SWCNT Under Electrostatic Actuation

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 ◽

10.1115/dscc2019-9171 ◽

2019 ◽

Author(s):

Dumitru I. Caruntu ◽

Ezequiel Juarez

Keyword(s):

Carbon Nanotubes ◽

Frequency Response ◽

Parametric Resonance ◽

Multiple Scales ◽

Van Der Waals ◽

Van Der Waals Force ◽

Beam Model ◽

Weakly Nonlinear ◽

Electrostatically Actuated ◽

Walled Carbon Nanotubes

Abstract This paper deals with electrostatically actuated Double-Walled Carbon Nanotubes (DWCNT) and Single-Walled Carbon Nanotubes (SWCNT) cantilever resonators. Frequency response of parametric resonance is investigated. Euler-Bernoulli cantilever beam model is used for both DWCNT and SWCNT. Electrostatic and viscous damping forces are applied on both types of resonators, DWCNT and SWCNT. In this investigation, soft AC voltage excitation is assumed. For the DWCNT, an intertube van der Waals force is present between the two concentric carbon nanotubes (CNTs), coupling their motion and acting as a nonlinear spring. The nonlinearities in the vibration are provided by the electrostatic (both SWCNT and DWCNT) and intertube van der Waals forces (DWCNT). The Method of Multiple Scales (MMS) is a perturbation method that provides uniformly valid approximations for weakly nonlinear systems. A Reduced-Order-Model (ROM) is developed and numerically solved using AUTO-07P (bifurcation and continuation software). Since large tip deflections are investigated in this paper, only coaxial vibration of the DWCNT is considered. Parametric resonance is investigated, as well as the influences of damping and voltage. Lastly, the effect of intertube van der Waals force on the bifurcation and stability of the DWCNT is reported.

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Parametric Resonance of MEMS Circular Plate Resonators

Volume 8: 27th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2015-46584 ◽

2015 ◽

Author(s):

Dumitru I. Caruntu ◽

Reynaldo Oyervides

Keyword(s):

Frequency Response ◽

Natural Frequency ◽

Circular Plate ◽

Parametric Resonance ◽

Elastic Plate ◽

Electrostatic Force ◽

Circular Plates ◽

Electrostatically Actuated ◽

Sensing Applications ◽

Ground Plate

This paper investigates parametric resonance of electrostatically actuated MEMS circular plates for resonator sensing applications. The system consists of a clamped circular elastic plate over a ground plate. Soft AC voltage of frequency near natural frequency of the plate gives the electrostatic force that leads the elastic plate into vibration, more specifically into parametric resonance which can be used afterwards for biosensing purposes. Frequency response and corresponding bifurcations are reported. The effects of damping and voltage are predicted.

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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 ◽

Method Of Multiple Scales ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Electrostatically Actuated ◽

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.

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Subharmonic Resonance of One Fourth Order of Electrostatically Actuated MEMS Circular Plates: Amplitude-Frequency Response

10.1115/detc2021-70415 ◽

2021 ◽

Author(s):

Dumitru I. Caruntu ◽

Julio Beatriz ◽

Miguel Martinez

Keyword(s):

Steady State ◽

Frequency Response ◽

Fourth Order ◽

Multiple Scales ◽

Method Of Multiple Scales ◽

Subharmonic Resonance ◽

Circular Plates ◽

Electrostatically Actuated ◽

Amplitude Frequency Response ◽

Steady State Solutions

Abstract This work deals with the amplitude-frequency response subharmonic resonance of 1/4 order of electrostatically actuated circular plates. The method of multiple scales is used to model the hard excitations and to predict the response. This work predicts that the steady state solutions are zero amplitude solutions, and non-zero amplitude solutions which consist of stable and unstable branches. The effects of parameters such as voltage and damping on the response are predicted. As the voltage increases, the non-zero amplitude solutions are shifted to lower frequencies. As the damping increases, the non-zero steady-state amplitudes are shifted to higher amplitudes, so larger initial amplitudes for the MEMS plate to reach non-zero steady-state amplitudes.

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Microelectromechanical Systems Cantilever Resonators Under Soft Alternating Current Voltage of Frequency Near Natural Frequency

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4028887 ◽

2015 ◽

Vol 137 (4) ◽

Cited By ~ 9

Author(s):

Dumitru I. Caruntu ◽

Martin W. Knecht

Keyword(s):

Frequency Response ◽

Natural Frequency ◽

Microelectromechanical Systems ◽

Multiple Scales ◽

Casimir Effect ◽

Alternating Current ◽

Electrostatically Actuated ◽

Current Voltage ◽

Fringe Effect ◽

Parametric Frequency

This paper deals with nonlinear-parametric frequency response of alternating current (AC) near natural frequency electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators. The model includes fringe and Casimir effects, and damping. Method of multiple scales (MMS) and reduced order model (ROM) method are used to investigate the case of weak nonlinearities. It is reported for uniform resonators: (1) an excellent agreement between the two methods for amplitudes less than half of the gap, (2) a significant influence of fringe effect and damping on bifurcation frequencies and phase–frequency response, respectively, (3) an increase of nonzero amplitudes' frequency range with voltage increase and damping decrease, and (4) a negligible Casimir effect at microscale.

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