A higher-order size-dependent beam model for nonlinear mechanics of fluid-conveying FG nanotubes incorporating surface energy

Abstract

Fluid-conveying tubes in nano scale present different mechanical behaviors from the macro tubes. A higher-order size-dependent beam model is developed coupling with the nonlocal stress, strain gradient effects, surface energy effects for flow-inducing post-buckling and free vibration analysis of the functionally graded nanotubes. Also, the slip flow effect is considered to modify the kinetic energy of the fluid. The governing equations of post-buckling and vibration are derived by the Hamilton variational principle in which the obtained post-buckling tube configuration is also the initial configuration for vibration analysis. The two-step perturbation method is extended to the nonlinear analysis of the fluid-conveying tubes, and a perturbation scheme is proposed. Subsequently, the influences of nano effects on post buckling, natural frequency and nonlinear vibration of the fluid-conveying nanotubes are studied. The imperfection sensitivity of the static and dynamic behaviors is also discussed. Numerical results reveal the dual influences of nano effects on the nonlinear behaviors and indicate the significance to consider the effects of surface energy, small scale and slip flow in nonlinear analyses of the fluid-conveying nanotubes in a comprehensive way.