Title :
Nonlinear vibration of fluid-conveying carbon nanotube using homotopy analysis method
Author :
Askari, Hassan ; Zhang, Dejing ; Esmailzadeh, Ebrahim
Author_Institution :
Univ. of Ontario Inst. of Technol., Oshawa, ON, Canada
Abstract :
Nonlinear vibration analysis of a single-walled carbon nanotube, using the Eringen nonlocal elasticity and Euler-Bernoulli beam theories, is carried out. Pasternak-type foundation and the simply-supported boundary conditions are assumed for the carbon nanotube and the governing equation of motion is developed using those theories. The Galerkin method is utilized to obtain the nonlinear ordinary differential equation of vibration of the single-walled carbon nanotube and the homotopy analysis method is employed to determine its nonlinear natural frequency. A parametric sensitivity study is then carried out. Few of the parameters were the axial tension, nonlocal parameter, fluid velocity and the foundation stiffness. The parametric study is mainly focused on the nonlinear natural frequency of single-walled carbon nanotube. Finally, a numerical simulation is carried out to determine the accuracy of the obtained results. Furthermore, an elliptical integral is utilized to verify the nonlinear natural frequency, which was obtained using the homotopy analysis method.
Keywords :
Galerkin method; carbon nanotubes; elasticity; nonlinear differential equations; vibrations; C; Eringen nonlocal elasticity theory; Euler-Bernoulli beam theory; Galerkin method; Pasternak-type foundation; fluid-conveying carbon; homotopy analysis; nonlinear natural frequency; nonlinear ordinary differential equation; nonlinear vibration analysis; numerical simulation; single-walled carbon nanotube; Boundary conditions; Carbon nanotubes; Differential equations; Equations; Fluids; Mathematical model; Vibrations;
Conference_Titel :
Nanotechnology (IEEE-NANO), 2013 13th IEEE Conference on
Conference_Location :
Beijing
Print_ISBN :
978-1-4799-0675-8
DOI :
10.1109/NANO.2013.6720962