On nonlinear behavior and buckling of fluid-transporting nanotubes

A general nonlinear nonlocal model for supported nanotubes conveying fluid is developed. Considering the geometric nonlinearity associated with the mid-plane stretching of the nanotube, the extended Hamilton’s principle is used to derive this general model based on Eringen’s nonlocal elasticity theory. Analytical solutions for the nonlinear responses of the nanotube are obtained from the constructed nonlinear equation. It is shown that the presence of the nonlocal effect tends to decrease the critical flow velocity and increase the buckled static displacement of the nanotube. It is also demonstrated that the nonlocal effect has a significant impact on the pre- and post-buckling natural frequencies of the nanotube while the mass ratio mainly influences the post-buckling frequencies and the geometric nonlinearity term has no effect on these frequencies of the nanotube.