Nonlinear mechanics of nanotubes conveying fluid

A nonlocal strain gradient elasticity approach is proposed for the mechanical behaviour of fluid-conveying nanotubes; a nonlinear analysis, incorporating stretching, is conducted for a model based on both a nonlocal theory along with a strain gradient one. A clamped-clamped nanotube conveying fluid, as a conservative gyroscopic nanosystem, is considered and the motion energy and size-dependent potential energy are developed via use of constitutive and strain-displacement relations. An energy minimisation is conducted via Hamilton's method for an oscillating nanotube subject to external forces. This gives the nonlinear equation of the motion which is reduced to a high DOF system via Galerkin's technique. As many nanodevices operate near resonance, the resonant motions are obtained using a frequency-continuation method. The effect of different nanosystem/fluid parameters, including fluid/solid interface and the flow speed, on the nonlinear resonance is analysed.