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.

Voltage Response of Parametric Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation

2017 ◽  
Author(s):  
Ezequiel Juarez ◽  
Dumitru I. Caruntu ◽  
Young-Gil Park
Keyword(s):  
Carbon Nanotube ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Van Der Waals ◽  
Voltage Response ◽  
First Order ◽  
Electrostatically Actuated ◽  
First Order Method ◽  
Euler Bernoulli Beam ◽  
Multiple Scales Solution

In this paper, the Method of Multiple Scales is used to investigate the influences of damping and detuning frequency parameters on the amplitude-voltage 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. Herein, the coaxial case is investigated, which eliminates the influence of the cubic van der Waals in the first-order solution. The double-walled carbon nanotube structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the double-walled carbon nanotube is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order Method of Multiple Scales solution. The importance of the results in this paper are the effect of damping and detuning frequency on the Hopf bifurcations, as these define the intervals of voltage for nonzero amplitudes.

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.

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.

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.

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

2017 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Nonlinear Behavior ◽  
Van Der Waals Forces ◽  
Electrostatic Actuation ◽  
Beam Model ◽  
Electrostatically Actuated

This paper deals with electrostatically actuated Double Walled Carbon Nanotubes (DWCNT) cantilevered resonators. The governing equations for the motion of the DWCNT are derived through Euler-Bernoulli beam model assumptions that account for inertial and viscoelastic effects. The DWCNT is a specific type of multi-walled carbon nanotube (MWCNT) that is comprised of two coaxially concentric carbon nanotubes. Electrostatic, damping, and intertube van der Waals forces act on the outer tube of the DWCNT, while only intertube van der Waals force acts on the inner tube. A soft AC voltage provides the electrostatic actuation. The nonlinear behavior and phenomena in the system are provided by the electrostatic and intertube van der Waals forces. The DWCNT is subjected to nonlinear parametric dynamics. The Method of Multiple Scales (MMS) is employed to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude response is found in the case of parametric resonance. The resulting nonlinear dynamic behavior is important to improve DWCNT resonator sensitivity in the application of mass sensing.

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

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.

Casimir and Van Der Waals Effects on Parametric Resonance of Bio-NEMS Circular Plate Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Frequency Response ◽  
Parametric Resonance ◽  
Elastic Plate ◽  
Electrostatic Force ◽  
Van Der Waals ◽  
Circular Plates ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Fixed Electrode ◽  
Electrode Plate

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.

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.

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.

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