Liu Chenxin
Huazhong University of Science and Technology
This is Master Chenxin Liu. She is a postgraduate student from Huazhong University of Science and Technology in Wuhan, China. She mainly research on nonlinear behavior of carbon nanotubes.
Abstract
There are many previous papers simulate the CNT conveying fluid which assume the longitudinal shape of the nanotube is entirely straight. However, the photos taken by transmission electron microscopes show that the CNT usually present curvature along their length, which influences their dynamical behavior efficiently. Motivated by the lack of study on the imperfection CNT, we will investigate the nonlinear dynamics of geometrical imperfect CNT.
In this research, we focus on transverse vibration of a single-walled carbon nanotube conveying fluid with supported ends based on the nonlocal elasticity theory and Timoshenko model. This CNT is assumed to be embedded in a Pasternak foundation and have a slight curvature initially as geometrical imperfection. Hamilton’s principle is applied to get the governing equation in this case, which considers stretching, large deformation and imperfection nonlinearities. Then, the Galerkin method is adopted to discretize the nonlinear governing equation. Eventually, the numerical results are obtained by Runge-Kutta algorithm. Stability, bifurcation, vibration frequencies and response behavior of the nanotube are obtained by analytical solutions.
The obtained results reveal that at high flow velocities, nonlinearity of the model become more important, especially for a slightly curved nanotube. Moreover, the existence of the geometrical imperfection and the surrounding elastic medium causes the natural frequency to increase while under the same flow velocity, which implies the rise of critical velocity. It is also demonstrated that the nonlocal parameter decrease the buckling natural frequency and critical velocity. According to the bifurcation diagram, the results show that the local parameter and geometrical imperfection have significant impact on the maximum amplitude of the oscillation. As the local parameter and initial curvature increase, the maximum amplitude increase.
Keywords: nanotube conveying fluid; nonlinear model; nonlocal elasticity theory;Timoshenko beam; natural frequency; imperfection
