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

Van Der Waals ◽

Voltage Response ◽

First Order ◽

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.

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

Volume 4B: Dynamics, Vibration, and Control ◽

10.1115/imece2017-70649 ◽

2017 ◽

Author(s):

Dumitru I. Caruntu ◽

Ezequiel Juarez

Keyword(s):

Carbon Nanotube ◽

Frequency Response ◽

Multiple Scales ◽

Van Der Waals ◽

First Order ◽

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.

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 7: 5th International Conference on Micro- and Nanosystems; 8th International Conference on Design and Design Education; 21st Reliability, Stress Analysis, and Failure Prevention Conference ◽

On Electrostatically Actuated CNT Bio-Sensors

10.1115/detc2011-48379 ◽

2011 ◽

Author(s):

Dumitru I. Caruntu ◽

Cone S. Salinas Trevino

Keyword(s):

Carbon Nanotubes ◽

Multiple Scales ◽

Van Der Waals ◽

Primary Resonance ◽

Mass Detection ◽

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.

Volume 3: Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy ◽

Primary Resonance Voltage Response of Electrostatically Actuated M/NEMS Circular Plate Resonators

10.1115/dscc2014-6277 ◽

2014 ◽

Author(s):

Dumitru I. Caruntu ◽

Reynaldo Oyervides

Keyword(s):

Casimir Force ◽

Multiple Scales ◽

Excitation Frequency ◽

Primary Resonance ◽

Voltage Response ◽

Circular Plates ◽

Amplitude Response ◽

Weakly Nonlinear ◽

Electrostatically Actuated

This paper investigates the voltage-amplitude response of soft AC electrostatically actuated M/NEMS clamped circular plates. AC frequency is near half natural frequency of the plate. This results in primary resonance. The system is analytically modeled using the Method of Multiple Scales (MMS). The system is assumed weakly nonlinear. The behavior of the system including pull-in instability as the AC voltage is swept up and down while the excitation frequency is constant is reported. The effects of detuning frequency, damping, Casimir force, and van der Waals force are reported as well.

Volume 5: 6th International Conference on Micro- and Nanosystems; 17th Design for Manufacturing and the Life Cycle Conference ◽

CNT Cantilevers Under Soft AC Actuation of Frequency Near Half Natural Frequency for Bio-Sensing Applications

10.1115/detc2012-70324 ◽

2012 ◽

Author(s):

Dumitru I. Caruntu ◽

Le Luo

Keyword(s):

Phase Behavior ◽

Multiple Scales ◽

Van Der Waals ◽

Mass Detection ◽

Sensing Applications ◽

Carbon Nano Tubes ◽

Ground Plate ◽

Frequency Phase

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers for bio-sensing applications. Four forces act on the CNT cantilever, namely electrostatic, elastostatic, 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) is used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behavior are reported. The CNT bio-sensor is to be used for mass detection applications.

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.

Volume 3: Modeling and Validation; Multi-Agent and Networked Systems; Path Planning and Motion Control; Tracking Control Systems; Unmanned Aerial Vehicles (UAVs) and Application; Unmanned Ground and Aerial Vehicles; Vibration in Mechanical Systems; Vibrations and Control of Systems; Vibrations: Modeling, Analysis, and Control ◽

Voltage Response for Parametrically Actuated MEMS Cantilever Beam Using Homotopy Analysis Method and Method of Multiple Scales

10.1115/dscc2018-9012 ◽

2018 ◽

Author(s):

Christopher Reyes ◽

Dumitru I. Caruntu

Keyword(s):

Parametric Resonance ◽

Homotopy Analysis Method ◽

Multiple Scales ◽

Van Der Waals ◽

Excitation Frequency ◽

Voltage Response ◽

Analysis Method ◽

Softening Effect ◽

Homotopy Analysis

The purpose of this paper is to investigate the nonlinear dynamics governing the behavior of electrostatically actuated micro electro mechanical systems (MEMS) cantilever undergoing parametric resonance. The MEMS consists of a cantilever parallel to a ground plate. The beam is actuated via an A/C voltage with excitation frequency near first natural frequency of the cantilever. The model includes damping, electrostatic, and Casimir (or van der Waals) forces. The electrostatic force is modeled to include the fringe effect. The amplitude-voltage response of the parametric resonance and the effects of varying the magnitudes of the fringe, Casimir (or Van der Waals), and damping forces along with varying the detuning parameter are reported. The response is obtained using two different methods, namely the method of multiple scales (MMS), and the homotopy analysis method (HAM). In this study approximations up to a 2nd order HAM are used. HAM is a deformation technique that begins with an initial guess and continuously deforms it to the exact answer. For the 1st Order HAM, a softening effect is reported. The 1st Order HAM matches the MMS results in low amplitude and begins to soften and deviate away from the MMS solution in higher amplitudes. For the 2nd Order HAM deformation the softening effect is slightly more pronounced with a slightly lower prediction of the maximum deflection of the cantilever tip. For the 2nd order deformation solution the stable branch of the amplitude-voltage response obtained by the HAM shifts leftward from the MMS solution with the unstable branches between the two methods continue to agree in low amplitudes and deviate in high amplitudes. As a remark, the higher order HAM solutions are obtained symbolically with the software Mathematica and numerically ran with the software Matlab.

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

Volume 8: 29th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2017-67367 ◽

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.

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

Volume 9: Mechanics of Solids, Structures, and Fluids ◽

10.1115/imece2019-11187 ◽

2019 ◽

Author(s):

Dumitru I. Caruntu ◽

Ezequiel Juarez

Keyword(s):

Frequency Response ◽

Multiple Scales ◽

Amplitude Ratio ◽

Van Der Waals ◽

Primary Resonance ◽

Strong Nonlinearity ◽

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.

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 ◽

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.