Clamped-Free Single-Walled Carbon Nanotube-Based Mass Sensor Treated as Bernoulli–Euler Beam

2011 ◽  
Vol 2 (2) ◽  
Author(s):  
I. Elishakoff ◽  
C. Versaci ◽  
N. Maugeri ◽  
G. Muscolino
Keyword(s):  
Exact Solution ◽  
Carbon Nanotube ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Mass Sensor ◽  
Euler Beam ◽  
Attached Bacterium ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
The Finite Difference Method

In this study, we investigate the vibrations of the cantilever single-walled carbon nanotube (SWCNT) with attached bacterium on the tip in view of developing the sensor. This sensor will be able to help to identify the bacterium or virus that may be attached to the SWCNT. Two cases are considered: These are light or heavy bacteria attached to the nanotube. The problem is solved by the exact solution, the finite difference method, and the Bubnov–Galerkin method.

scholarly journals Buckling of double-walled carbon nanotubes

2012 ◽  
Vol 34 (4) ◽  
pp. 217-224 ◽  
Author(s):  
Isaac Elishakoff ◽  
Kévin Dujat ◽  
Maurice Lemaire
Keyword(s):  
Carbon Nanotubes ◽  
Exact Solution ◽  
Approximate Solution ◽  
Carbon Nanotube ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Simply Supported ◽  
The Finite Difference Method ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this note we deal with the approximate solution of the buckling problem of a clamped-free double-walled carbon nanotube. First the finite difference method is utilized to solve this case. Then this approach is verified by solving the buckling problem of a double-walled carbon nanotube that is simply supported at both ends for which the exact solution is available.

Nonlinear Dynamic Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

2011 ◽  
Vol 2 (4) ◽  
Author(s):  
Anand Y. Joshi ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Dynamic Response ◽  
Beam Theory ◽  
Central Plane ◽  
Mass Sensor ◽  
Poincaré Maps ◽  
Single Walled Carbon Nanotube ◽  
Poincare Maps ◽  
Single Walled Carbon

In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. This paper deals with the nonlinear vibration analysis of a wavy single-walled carbon nanotube based mass sensor, which is doubly clamped at a source and a drain. Nonlinear oscillations of a single-walled carbon nanotube excited harmonically near its primary resonance are considered. The carbon nanotube is excited by the addition of an excitation force. The modeling is carried out using the elastic continuum beam theory concept, which involves stretching of the central plane and phenomenological damping. This model takes into account the existence of waviness in carbon nanotubes. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass and the geometric imperfections of carbon nanotube. Poincaré maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

A numerical study by using the Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation

2018 ◽  
Vol 11 (08) ◽  
pp. 1850099 ◽  
Author(s):  
Mohamed M. Khader ◽  
Khaled M. Saad
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Collocation Method ◽  
Numerical Study ◽  
Fisher Equation ◽  
Chebyshev Collocation Method ◽  
The Third ◽  
The Finite Difference Method

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.

scholarly journals 1D Generalised Burgers-Huxley: Proposed Solutions Revisited and Numerical Solution Using FTCS and NSFD Methods

2022 ◽  
Vol 7 ◽  
Author(s):  
Appanah R. Appadu ◽  
Yusuf O. Tijani
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Difference Method ◽  
Huxley Equation ◽  
The Finite Difference Method ◽  
A Minor

In this paper, we obtain the numerical solution of a 1-D generalised Burgers-Huxley equation under specified initial and boundary conditions, considered in three different regimes. The methods are Forward Time Central Space (FTCS) and a non-standard finite difference scheme (NSFD). We showed the schemes satisfy the generic requirements of the finite difference method in solving a particular problem. There are two proposed solutions for this problem and we show that one of the proposed solutions contains a minor error. We present results using FTCS, NSFD, and exact solution as well as show how the profiles differ when the two proposed solutions are used. In this problem, the boundary conditions are obtained from the proposed solutions. Error analysis and convergence tests are performed.

Sign in / Sign up

Export Citation Format

Share Document