Reduced Order Model of Coaxial Vibrations of Electrostatically Actuated Double Wall Carbon Nanotubes: Frequency Response of Primary Resonance

2018 ◽  
Author(s):  
Ezequiel Juarez ◽  
Dumitru I. Caruntu
Keyword(s):  
Carbon Nanotubes ◽  
Frequency Response ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Approximate Solutions ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Steady State Solutions

In this paper, the Reduced Order Method (ROM) and the Method of Multiple Scales (MMS) are used to investigate the influences of dimensionless damping and voltage parameters on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube (DWCNT). The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. Soft AC excitation and small viscous damping forces are assumed. Herein, the coaxial case is investigated. In this mode of vibration, the outer and inner carbon nanotubes move synchronously (in-phase) with the same maximum tip deflection. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order MMS solution. The analytical approximate solutions provided by MMS are validated numerically by two-term (2T) Time Reponses and AUTO-07P. The two methods in this paper are found to be in excellent agreement at lower amplitudes. Additionally, the two methods are assessed for their advantages and limitations. The importance of the results in this paper are the effect of damping and voltage on the stability of the DWCNT vibration.

Frequency Response of Parametric Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation for Noncoaxial Vibration

2017 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotube ◽  
Frequency Response ◽  
Multiple Scales ◽  
Van Der Waals ◽  
First Order ◽  
Electrostatically Actuated ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Steady State Solutions ◽  
High Length

In this paper, the Method of Multiple Scales is used to investigate the influences of dimensionless damping and voltage parameters on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube. The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. Soft AC excitation and small viscous damping forces are assumed. Herein, the noncoaxial case is investigated at near-zero amplitude conditions in the free vibration, which eliminates the influence of the cubic van der Waals in the first-order solution. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order MMS solution. The importance of the results in this paper are the effect of damping and detuning frequency on the stability of the DWCNT vibration.

Comparison of Frequency Response of Primary Resonance of DWCNT and CNT Resonators Under Electrostatic Actuation

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Electrostatic Actuation ◽  
Amplitude Response ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Abstract This paper deals with the frequency-amplitude response of primary resonance of electrostatically actuated Double-Walled Carbon Nanotubes (DWCNT) and Single-Walled Carbon Nanotubes (SWCNT) cantilever resonators. Their responses are compared. Both the DWCNT and SWCNT are modeled as Euler-Bernoulli cantilever beams. Electrostatic and damping forces are applied on both types of resonators. An AC voltage provides a soft electrostatic actuation. For the DWCNT, intertube van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes and acting as a nonlinear spring between the two carbon nanotubes. Electrostatic (for SWCNT and DWCNT) and intertube van der Waals (for DWCNT) forces are nonlinear. Both resonators undergo nonlinear parametric excitation. The Method of Multiple Scales (MMS) is used to investigate the systems under soft excitations and weak nonlinearities. A 2-Term Reduced-Order-Model (ROM) is numerically solved for stability analysis using AUTO-07P, a continuation and bifurcation software. The coaxial vibrations of DWCNT are considered in this work, in order to draw comparisons between DWCNT and SWCNT. Effects of damping and voltage of the frequency-amplitude response are reported.

Noncoaxial Vibration of Electrostatically Actuated DWCNT: Frequency Response of Primary Resonance

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Amplitude Ratio ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Strong Nonlinearity ◽  
Electrostatically Actuated ◽  
Time In Literature ◽  
First Time ◽  
Euler Bernoulli Beam

Abstract In this paper, the Method of Multiple Scales (MMS) is used to investigate the influences of the nonlinear intertube van der Waals coefficient, dimensionless damping, and voltage on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube (DWCNT). The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. For perturbation, a small viscous damping and soft AC actuation are assumed for numerical simulation. For the first time in literature, forced vibration of the noncoaxial (out-of-phase) case is investigated. In this mode of vibration, the outer and inner carbon nanotubes move at ultra-high frequency in opposite direction, i.e., negative amplitude ratio. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is assumed to have a high length-diameter ratio. The results shown assume steady-state solutions in the second-order MMS solution. The importance of the results in this paper are the effect of the strong nonlinearity of the van der Waals coefficient, damping, and voltage on the the DWCNT vibration.

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.

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.

On Primary Resonance of Electrostatically Actuated Double Walled Carbon Nanotube Cantilever Biosensors

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Van Der Waals Forces ◽  
Mass Sensing ◽  
Electrostatically Actuated ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

This paper investigates electrostatically actuated Double Walled Carbon Nanotubes (DWCNT) cantilever biosensors using the Method of Multiple Scales (MMS) and the Harmonic Balance Method (HBM). Forces acting on the outer tube of the DWCNT are electrostatic, damping, and van der Waals, while only van der Waals acts on the inner tube. The electrostatic actuation is provided by a soft AC voltage. Van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes; herein, for modal coordinate transformation, only the linear term of the van der Waals force will be considered. The nonlinearity of the motion is produced by the electrostatic and van der Waals forces. The DWCNT undergoes nonlinear parametric dynamics. MMS is employed to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude response is found in the case of primary resonance. DWCNTs are modelled after the Euler-Bernoulli cantilever beam. The expected nonlinear dynamic behavior is important to improve DWCNT resonator sensitivity in the application of mass sensing.

On Electrostatically Actuated CNT Bio-Sensors

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Cone S. Salinas Trevino
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Mass Detection ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Ground Plate ◽  
Frequency Phase

This paper deals with electrostatically actuated Carbon NanoTubes (CNT) cantilevers for bio-sensing applications. There are three kinds of forces acting on the CNT cantilever: electrostatic, elastostatic, and van der Waals. 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 dynamics is nonlinear parametric. The method of multiple scales is used to investigate the system under soft excitations and/or weakly nonlinearities. The frequency-amplitude and frequency-phase behavior are found in the case of primary resonance. The CNT bio-sensor is to be used for mass detection applications.

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

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.

Reduced Order Model of Electrostatically Actuated Carbon Nanotube Cantilever Biosensors for Primary Resonance

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate

This paper investigates electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers biosensors using the Reduced Order Model (ROM) method. Forces acting on the CNT are electrostatic, damping, and van der Waals. The electrostatic actuation is given by soft AC voltage. Van der Waals forces are significant for gaps between the CNT and a ground plate lower than 100 nm. Both forces electrostatic and van der Waals are nonlinear. CNT undergoes nonlinear parametric dynamics. ROM is used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude response is found in the case of primary resonance and compared to the Method of Multiple Scales (MMS). The CNT biosensor is to be used for mass detection applications.

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