A Hybrid Power Series Artificial Bee Colony Algorithm to Obtain a Solution for Buckling of Multiwall Carbon Nanotube Cantilevers Near Small Layers of Graphite Sheets

A hybrid power series and artificial bee colony algorithm (PS-ABC) method is applied to solve a system of nonlinear differential equations arising from the distributed parameter model of multiwalled carbon nanotube (MWCNT) cantilevers in the vicinity of thin and thick graphite sheets subject to intermolecular forces. The intermolecular forces are modeled using van derWaals forces. A trial solution of the differential equation is defined as sum of two polynomial parts. The first part satisfies the boundary conditions and does contain two adjustable parameters. The second part is constructed as not to affect the boundary conditions, which involves adjustable parameters. The ABC method is applied to find adjustable parameters of trial solution (in first and second part). The obtained results are compared with numerical results as well as analytical solutions those reported in the literature. The results of the presented method represent a remarkable accuracy in comparison with numerical results. The minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular forces, as important parameters in pull-in instability of MWCNT actuator, are evaluated by obtained power series.

[1]  T. Goswami,et al.  Carbon nanotubes – Production and industrial applications , 2007 .

[2]  Robert D. Russell,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[3]  G. L. Klimchitskaya,et al.  van der Waals and Casimir interactions between atoms and carbon nanotubes , 2008, 0802.1276.

[4]  Andrew J. Meade,et al.  The numerical solution of linear ordinary differential equations by feedforward neural networks , 1994 .

[5]  A. Rinzler,et al.  Carbon nanotube actuators , 1999, Science.

[6]  Raja Muhammad Asif Zahoor,et al.  Swarm Intelligence for the Solution of Problems in Differential Equations , 2009, 2009 Second International Conference on Environmental and Computer Science.

[7]  S. Dong,et al.  A multi-wall carbon nanotube (MWCNT) relocation technique for atomic force microscopy (AFM) samples. , 2005, Ultramicroscopy.

[8]  M. Hodak,et al.  Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential , 2000 .

[9]  M. Ghalambaz,et al.  A NEW APPROACH TO SOLVE BLASIUS EQUATION USING PARAMETER IDENTIFICATION OF NONLINEAR FUNCTIONS BASED ON THE BEES ALGORITHM (BA) , 2011 .

[10]  Alaeddin Malek,et al.  Numerical solution for high order differential equations using a hybrid neural network - Optimization method , 2006, Appl. Math. Comput..

[11]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[12]  Horacio Dante Espinosa,et al.  EXPERIMENTS AND MODELING OF CARBON NANOTUBE-BASED NEMS DEVICES , 2005 .

[13]  W. Lin,et al.  Casimir effect on the pull-in parameters of nanometer switches , 2005 .

[14]  M. Grujicic,et al.  Computational analysis of the lattice contribution to thermal conductivity of single-walled carbon nanotubes , 2005 .

[15]  Seiji Akita,et al.  Nanotweezers consisting of carbon nanotubes operating in an atomic force microscope , 2001 .

[16]  M. A. Behrang,et al.  A New Solution for Natural Convection of Darcian Fluid about a Vertical Full Cone Embedded in Porous Media Prescribed Wall Temperature by using a Hybrid Neural Network-Particle Swarm Optimization Method , 2011 .

[17]  Chunyu Li,et al.  Sensors and actuators based on carbon nanotubes and their composites: A review , 2008 .

[18]  N. Aluru,et al.  Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches , 2002 .

[19]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[20]  Ado Jorio,et al.  UNUSUAL PROPERTIES AND STRUCTURE OF CARBON NANOTUBES , 2004 .

[21]  Dimitrios I. Fotiadis,et al.  Artificial neural networks for solving ordinary and partial differential equations , 1997, IEEE Trans. Neural Networks.

[22]  He died because he was wearing the wrong color sneakers: Some thoughts on the unpopularity of intellect and the issue of difference in today's society (remarks of the special issue editor) , 1994 .

[23]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[24]  Zhen Yao,et al.  Carbon Nanotube Single‐Electron Transistors at Room Temperature. , 2001 .

[25]  Hyuk Lee,et al.  Neural algorithm for solving differential equations , 1990 .

[26]  M. A. Behrang,et al.  A Hybrid Neural Network and Gravitational Search Algorithm (HNNGSA) Method to Solve well known Wessinger's Equation , 2011 .

[27]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[28]  Mahmoud M. Farag,et al.  Carbon nanotube reinforced composites: Potential and current challenges , 2007 .

[29]  Mohamadreza Abadyan,et al.  An Approximate Solution for a Simple Pendulum beyond the Small Angles Regimes Using Hybrid Artificial Neural Network and Particle Swarm Optimization Algorithm , 2011 .

[30]  Dervis Karaboga,et al.  A modified Artificial Bee Colony algorithm for real-parameter optimization , 2012, Inf. Sci..

[31]  M. Abadyan,et al.  New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets , 2011 .