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.

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 Primary Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation

2016 ◽  
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 ◽  
Electrostatic Actuation ◽  
Van Der Waals Force ◽  
Order Problem ◽  
Electrostatically Actuated

This paper deals with electrostatically actuated Double Walled Carbon Nanotubes (DWCNT) cantilever resonators. DWCNTs are modeled as Euler-Bernoulli cantilever beams. Electrostatic, damping, and van der Waals, forces act on the outer tube of the DWCNT, while only van der Waals force acts on the inner tube. A soft AC voltage provides the electrostatic actuation. Van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes. The nonlinearities in the system are given by the electrostatic and van der Waals forces. The DWCNT undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS) is employed to investigate the system under soft excitations and/or weak nonlinearities. A modal coordinate transformation, in which only the linear term of the van der Waals force are considered, and the Harmonic Balance Method (HBM), are used to solve the zero-order problem. Then the frequency-amplitude response is found in the case of primary resonance. The expected nonlinear dynamic behavior is important to improve DWCNT resonator sensitivity in the application of mass sensing.

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.

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.

Nonlinear Parametric Resonance for NEMS and MEMS Biosensor Applications

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Parametric Resonance ◽  
Nonlinear Behavior ◽  
Electrostatic Actuation ◽  
Mass Detection ◽  
Actuation Frequency ◽  
Electrostatically Actuated ◽  
Biosensor Applications

This paper deals with electrostatically actuated resonator micro- and nano-sensor for mass detection for applications in medicine and biology. Nonlinear parametric resonance of the sensor when the electrostatic actuation frequency is near natural frequency of the system is investigated. Mass deposition is included and its effect on the nonlinear behavior of the resonator is predicted.

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.

On Nonlinear Dynamics of Nanotweezers

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.

Casimir and Van der Waals Effects on Voltage Response of Electrostatically Actuated MEMS/NEMS Plates

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides ◽  
Valeria Garcia
Keyword(s):  
Natural Frequency ◽  
Parametric Resonance ◽  
Electrostatic Force ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Amplitude Response ◽  
Electrostatically Actuated ◽  
Ground Plate

This paper deals with electrostatically actuated MEMS plates. The model consists of a flexible MEMS plate above a parallel ground plate. An AC voltage of frequency near natural frequency of the plate provides the electrostatic force that actuates the flexible MEMS plate. This leads to parametric resonance. The effect of Casimir and/or van der Waals forces on the voltage-amplitude response of the plate is investigated.

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

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Parametric Resonance ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
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.

scholarly journals Buckling and Vibration of Carbon Nanotubes Embedded in Polyethylene Polymers

2012 ◽  
Vol 3 (2) ◽  
Author(s):  
Dai Shi ◽  
Quan Wang ◽  
Vijay K. Varadan ◽  
Wenhui Duan
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Molecular Mechanics ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Buckling Instability ◽  
Resonance Frequencies

The discovery of buckling instability and vibration of polyethylene (PE)/carbon nanotube (CNT) matrices is reported by molecular mechanics simulations. The buckling strains and the resonance frequencies are found to decrease with an increase in the number of polyethylene chains in the polyethylene/carbon nanotube matrices. The van der Waals forces between the polyethylene chains and the carbon nanotube in matrices are investigated to provide physical interpretations on the findings.

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