On the Oscillation Frequency of Ellipsoidal Fullerene–Carbon Nanotube Oscillators

2012 ◽  
Vol 3 (1) ◽  
Author(s):  
R. Ansari ◽  
F. Sadeghi
Keyword(s):  
Oscillation Frequency ◽  
Carbon Nanostructures ◽  
Initial Conditions ◽  
Interaction Force ◽  
Oscillatory Behavior ◽  
Continuum Approximation ◽  
Geometrical Parameters ◽  
System Variables ◽  
Walled Carbon Nanotubes ◽  
Analytical Expressions

There are many new nanomechanical devices created based on carbon nanostructures among which gigahertz oscillators have generated considerable interest to many researchers. In the present paper, the oscillatory behavior of ellipsoidal fullerenes inside single-walled carbon nanotubes is studied comprehensively. Utilizing the continuum approximation along with Lennard–Jones potential, new semi-analytical expressions are presented to evaluate the potential energy and van der Waals interaction force of such systems. Neglecting the frictional effects, the equation of motion is directly solved on the basis of the actual force distribution between the interacting molecules. In addition, a semi-analytical expression is given to determine the oscillation frequency into which the influence of initial conditions is incorporated. Based on the newly derived expression, a thorough study on the various aspects of operating frequencies under different system variables such as geometrical parameters and initial conditions is conducted. Based on the present study, some new aspects of such nano-oscillators have been disclosed.

Oscillation of C60 Fullerene in Carbon Nanotube Bundles

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
R. Ansari ◽  
F. Sadeghi ◽  
A. Alipour
Keyword(s):  
Carbon Nanotube ◽  
Potential Energy ◽  
Oscillation Frequency ◽  
Initial Conditions ◽  
Van Der Waals ◽  
Oscillatory Behavior ◽  
C60 Fullerene ◽  
Continuum Approximation ◽  
Geometrical Parameters ◽  
Energy Potential

This paper aims to present a thorough investigation into the mechanics of a C60 fullerene oscillating within the center of a carbon nanotube bundle. To model this nanoscale oscillator, a continuum approximation is used along with a classical Lennard–Jones potential function. Accordingly, new semianalytical expressions are given in terms of single integrals to evaluate van der Waals potential energy and interaction force between the two nanostructures. Neglecting the frictional effects and using the actual van der Waals force distribution, the equation of motion is directly solved. Furthermore, a new semianalytical formula is derived from the energy equation to determine the precise oscillation frequency. This new frequency formula has the advantage of incorporating the effects of initial conditions and geometrical parameters. This enables us to conduct a comprehensive study of the effects of significant system parameters on the oscillatory behavior. Based upon this study, the variation of oscillation frequency with geometrical parameters (length of tubes or number of tubes in bundle) and initial energy (potential energy plus kinetic energy) is shown.

scholarly journals A Review of Geometry, Construction and Modelling for Carbon Nanotori

2019 ◽  
Vol 9 (11) ◽  
pp. 2301 ◽  
Author(s):  
Pakhapoom Sarapat ◽  
James Hill ◽  
Duangkamon Baowan
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanostructures ◽  
Single Walled Carbon Nanotubes ◽  
Continuum Approximation ◽  
Interaction Energies ◽  
Jones Potential ◽  
Lennard Jones ◽  
Walled Carbon Nanotubes ◽  
Analytical Expressions ◽  
The Continuum

After the discovery of circular formations of single walled carbon nanotubes called fullerene crop circles, their structure has become one of the most researched amongst carbon nanostructures due to their particular interesting physical properties. Several experiments and simulations have been conducted to understand these intriguing objects, including their formation and their hidden characteristics. It is scientifically conceivable that these crop circles, nowadays referred to as carbon nanotori, can be formed by experimentally bending carbon nanotubes into ring shaped structures or by connecting several sections of carbon nanotubes. Toroidal carbon nanotubes are likely to have many applications, especially in electricity and magnetism. In this review, geometry, construction, modelling and possible applications are discussed and the existing known analytical expressions, as obtained from the Lennard-Jones potential and the continuum approximation, for their interaction energies with other nanostructures are summarised.

Mechanics of Ellipsoidal Carbon Onions Inside Multiwalled Carbon Nanotubes

2012 ◽  
Vol 3 (1) ◽  
Author(s):  
F. Sadeghi ◽  
R. Ansari
Keyword(s):  
Carbon Nanotubes ◽  
Multiwalled Carbon Nanotubes ◽  
Oscillation Frequency ◽  
Direct Method ◽  
Van Der Waals ◽  
Oscillatory Behavior ◽  
Van Der Waals Interactions ◽  
Continuum Approximation ◽  
Multiwalled Carbon ◽  
Carbon Onions

On the basis of the continuum approximation along with Lennard–Jones potential function, new semi-analytical expressions are presented to evaluate the van der Waals interactions between an ellipsoidal fullerene and a semi-infinite single-walled carbon nanotube. Using direct method, these expressions are also extended to model ellipsoidal carbon onions inside multiwalled carbon nanotubes. In addition, acceptance and suction energies which are two noticeable issues for medical applications such as drug delivery are determined. Neglecting the frictional effects and by imposing some simplifying assumptions on the van der Waals interaction force, a simple formula is given to evaluate the oscillation frequency of ellipsoidal carbon onions inside multiwalled carbon nanotubes. Also, the effects of the number of tube shells and ellipsoidal carbon onion shells on the oscillatory behavior are examined. It is shown that there exists an optimal value for the number of tube shells beyond which the oscillation frequency remains unchanged.

ON THE MECHANICS OF ELLIPSOIDAL FULLERENES INSIDE OPEN CARBON NANOCONES: A NOVEL NUMERICAL APPROACH

NANO ◽  
2014 ◽  
Vol 09 (03) ◽  
pp. 1450034 ◽  
Author(s):  
R. ANSARI ◽  
F. SADEGHI ◽  
M. FAGHIH SHOJAEI
Keyword(s):  
Potential Energy ◽  
Fullerene Molecule ◽  
Interaction Force ◽  
Numerical Approach ◽  
Continuum Approximation ◽  
Vertex Angle ◽  
Geometrical Parameters ◽  
Operational Matrices ◽  
Carbon Nanocones ◽  
Open Cnc

In this research, mechanics of concentric ellipsoidal fullerenes inside open carbon nanocones (CNCs) is investigated. To this end, using continuum approximation in conjunction with Lennard-Jones (LJ) potential function, quadruple-integral expressions associated with van der Waals (vdW) potential energy and interaction force are first derived. For determination of these expressions, it is assumed that the fullerene molecule enters the open CNC through the small end or wide end. Thereafter, an efficient approach based on the differential quadrature (DQ) method is proposed to numerically evaluate the obtained quadruple integrals. The proposed method takes advantage of computing multidimensional integrals efficiently with using appropriate number of grid points. By introducing DQ-based operational matrices of differentiation and integration, the quadruple-integral expressions are estimated over their domains. Moreover, new semianalytical expressions are introduced in terms of triple integrals to evaluate vdW interactions. The validity and accuracy of the introduced numerical method are proved by comparing the results obtained through this method with ones achieved via the semianalytical expressions. The ease of implementation and quick answer of the demonstrated numerical solution enable us to comprehensively examine the effects of different geometrical parameters such as small end radius wide end radius and vertex angle of nanocone on the distributions of vdW potential energy and interaction force. The results reveal that the ellipsoidal fullerene undergoes an asymmetrical motion along the axis of open CNC.

Continuum study on the mechanics of ion-based carbon nanocones as gigahertz oscillators

2018 ◽  
Vol 233 (9) ◽  
pp. 3259-3276 ◽  
Author(s):  
F Sadeghi ◽  
R Ansari
Keyword(s):  
Potential Energy ◽  
Functional Groups ◽  
Oscillation Frequency ◽  
Electrostatic Interactions ◽  
Chloride Ion ◽  
Interaction Force ◽  
Separation Distance ◽  
Integration Scheme ◽  
Vertex Angle ◽  
Geometrical Parameters

There is a growing interest in the development of nanomechanical oscillators operating in the gigahertz range and beyond. This paper introduces a novel nano-oscillator based on a chloride ion inside an open carbon nanocone decorated by functional groups at both small and wide ends. Assuming that the carbon atoms and the electric charges of functional groups are evenly distributed over the surface and the two ends of nanocone, respectively, a continuum-based model is presented through which potential energy and interaction force are evaluated analytically. The van der Waals interactions between ion and nanocone are modeled by the 6–12 Lennard–Jones potential, while the electrostatic interactions between ion and two functional groups are modeled by the Coulomb potential. With respect to the proposed formulations, potential energy and interaction force distribution are presented by varying sign and magnitude of functional groups charge and geometrical parameters (size of small and wide ends of nanocone and its vertex angle). Using the fourth-order Runge–Kutta numerical integration scheme, the equation of motion is also solved to arrive at the time histories of separation distance and velocity of ion. An extensive study is performed to investigate the effects of sign and magnitude of functional groups charge, geometrical parameters, and initial conditions (initial separation distance and initial velocity) on the oscillatory behavior of ion-electrically charged open carbon nanocone oscillator. Numerical results demonstrate that the oscillation frequency of chloride ion inside an uncharged nanocone is respectively lower and higher than those generated inside a nanocone whose small end is decorated by positively and negatively charged functional groups. It is further shown that oscillation frequency is highly affected by the sign of electric charges distributed at the small end of nanocone.

Mechanics of metallic nanoparticles inside lipid nanotubes: Suction and acceptance energies

2016 ◽  
Vol 231 (13) ◽  
pp. 2540-2553 ◽  
Author(s):  
F Sadeghi ◽  
R Ansari ◽  
M Darvizeh
Keyword(s):  
Metallic Nanoparticles ◽  
Differential Quadrature Method ◽  
Van Der Waals ◽  
Van Der Waals Interactions ◽  
Continuum Approximation ◽  
Head Group ◽  
Geometrical Parameters ◽  
Lipid Nanotubes ◽  
Lipid Nanotube ◽  
Analytical Expressions

Lipid nanotubes with well-designed cylindrical structures, tunable dimensions and biocompatible membrane surfaces have found potential applications such as templates to create diverse one-dimensional nanostructures and nanocarriers for drug or gene delivery. In this regard, knowing the encapsulation process is of crucial importance for such developments. The aim of this paper is to study the suction and acceptance phenomena of metallic nanoparticles, and in particular silver and gold, inside lipid nanotubes using the continuum approximation and the 6–12 Lennard-Jones potential function. The nanoparticle is modelled as a perfect sphere and the lipid nanotube is assumed to comprise six layers, namely two head groups, two intermediate layers and two tail groups. Analytical expressions are derived through undertaking surface and volume integrals to evaluate van der Waals potential energy and interaction force of a nanoparticle entering a semi-infinite lipid nanotube. These expressions are then employed to determine the suction and acceptance energies of system. To ascertain the accuracy of the proposed analytical expressions, the multiple integrals of van der Waals interactions are evaluated numerically based on the differential quadrature method. A comprehensive study is conducted to get an insight into the effects of different geometrical parameters including radius of nanoparticles, innermost radius of lipid nanotube, head group and tail group thicknesses on the nature of suction and acceptance energies and van der Waals interactions. Numerical results show that maximum suction energy increases by enlarging the nanoparticle size, while it decreases by increasing the head group thickness or the tail group thickness. It is further found that gold nanoparticle experiences higher maximum suction energies inside lipid nanotubes compared to silver nanoparticle.

MULTI–INERT OSCILLATORY MECHANISM

2020 ◽  
Vol 2 ◽  
pp. 19-25
Author(s):  
I.P. POPOV
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Oscillation Frequency ◽  
Free Oscillation ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Harmonic Oscillations ◽  
Oscillatory Systems ◽  
Oscillatory Mechanism ◽  
Mutual Conversion

A mechanical oscillatory system with homogeneous elements, namely, with n massive loads (multi– inert oscillator), is considered. The possibility of the appearance of free harmonic oscillations of loads in such a system is shown. Unlike the classical spring pendulum, the oscillations of which are due to the mutual conversion of the kinetic energy of the load into the potential energy of the spring, in a multi–inert oscillator, the oscillations are due to the mutual conversion of only the kinetic energies of the goods. In this case, the acceleration of some loads occurs due to the braking of others. A feature of the multi–inert oscillator is that its free oscillation frequency is not fixed and is determined mainly by the initial conditions. This feature can be very useful for technical applications, for example, for self–neutralization of mechanical reactive (inertial) power in oscillatory systems.

On New Aspects of Nested Carbon Nanotubes as Gigahertz Oscillators

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
R. Ansari ◽  
B. Motevalli
Keyword(s):  
Carbon Nanotubes ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Interaction Force ◽  
Arbitrary Length ◽  
Oscillatory Frequency ◽  
Analytical Expression ◽  
System Parameters ◽  
The Core

Nested carbon nanotubes exhibit telescopic oscillatory motion with frequencies in the gigahertz range. In this paper, our previously proposed semi-analytical expression for the interaction force between two concentric carbon nanotubes is used to solve the equation of motion. That expression also enables a new semi-analytical expression for the precise evaluation of oscillation frequency to be introduced. Alternatively, an algebraic frequency formula derived based on the simplifying assumption of constant van der Waals force is also given. Based on the given formulas, a thorough study on different aspects of operating frequencies under various system parameters is conducted, which permits fresh insight into the problem. Some notable improvements over the previously drawn conclusions are made. The strong dependence of oscillatory frequency on system parameters including the extrusion distance and initial velocity of the core as initial conditions for the motion is shown. Interestingly, our results indicate that there is a special initial velocity at which oscillatory frequency is unique for any arbitrary length of the core. A particular relationship between the escape velocity (the minimum initial velocity beyond which the core will leave the outer nanotube) and this specific initial velocity is also revealed.

scholarly journals Simulation of rod vibrations process with an independent pendular suspension and vertical stabilization system

2018 ◽  
Vol 56 (4) ◽  
pp. 469-480
Author(s):  
I. S. Kruk ◽  
A. A. Tiunchik ◽  
V. Romanyuk
Keyword(s):  
Technological Process ◽  
Initial Conditions ◽  
Vertical Movement ◽  
Design Stage ◽  
Geometrical Parameters ◽  
Stabilization System ◽  
Special Approach ◽  
Rod Structures ◽  
Design And Testing

Continuous improvement of field sprayer design aimed at performance increase by increasing the working width, requires a special approach to ensure reliability of the supporting rod structure and quality of technological process. The question of rod vibrations, which arise when the driving systems copy field rough surface and abrupt changes in speed of the unit, remains topical. At the design stage of supporting structures of the rods, special attention is paid to the substantiation of its geometrical parameters in the longitudinal and transverse sections; studies of changes in the characteristics of vertical and horizontal vibrations, taking into account the method of the rod hanging and the system used for its stabilization. This allows to ensure the reliability of the rod design and the required quality of the technological process. The article proposes construction of the rod independent pendulum suspension on the sprayer frame and its stabilization system based on the use of damping elements. The analytical studies sequence system was developed for rod vibrations analysis, depending on initial conditions, parameters and characteristics of the used damping elements, under which they are effectively damped. It is shown that at certain numerical values of the geometrical parameters of the rod, the suspension and vibrations damping methods, not only the numerical values of the functions are changed, but also the functions themselves that describe the process of the rod's vertical movement, including cases of resonance. The obtained theoretical results can be used for design and testing of machines with rod working units and allow, at design stages, to simulate the process of movement of various rod structures from external excitatory forces, and to determine patterns of changes in the characteristics of damped vibrations using different damping elements and their installation parameters.

Free and Forced Response of an Axially Moving String Transporting a Damped Linear Oscillator

1993 ◽  
Author(s):  
W. D. Zhu ◽  
C. D. Mote
Keyword(s):  
Initial Conditions ◽  
Numerical Algorithms ◽  
Time History ◽  
Coupled System ◽  
Interaction Force ◽  
Forced Response ◽  
Linear Oscillator ◽  
Response Analysis ◽  
History Of ◽  
Axially Moving

Abstract The transverse response of a cable transport system, which is modelled as an ideal, constant tension string travelling at constant speed between two supports with a damped linear oscillator attached to it, is predicted for arbitrary initial conditions, external forces and boundary excitations. The exact formulation of the coupled system reduces to a single integral equation of Volterra type governing the interaction force between the string and the payload oscillator. The time history of the interaction force is discontinuous for non-vanishing damping of the oscillator. These discontinuities occur at the instants when transverse waves propagating along the string interact with the oscillator. The discontinuities are treated using the theory of distributions. Numerical algorithms for computing the integrals involving generalized functions and for solution of the delay-integral-differential equation are developed. Response analysis shows a discontinuous velocity history of the payload attachment point. Special conditions leading to absence of the discontinuities above are given.

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