Nonlinear size-dependent bending and forced vibration of internal flow-inducing pre- and post-buckled FG nanotubes

Abstract Fluid-conveying nanotubes are important components in nano-electromechanical systems requiring strict static and dynamic stiffness designs. The nonlinear bending and forced vibration of the fluid-conveying functionally graded nanotubes in pre- and post-buckling states are investigated. Based on Zhang–Fu’s refined displacement field, a comprehensive size-dependent nanotube model is established in which the nonlocal stress, strain gradient and surface energy effect are coupled in the constructive model. The nanotube is assumed simply supported at both ends and subjected to transverse uniform static or harmonic load. The two-step perturbation technique is extended to obtain the post-buckling equilibrium paths, providing the initial configurations for bending and resonance analysis. According to the two symmetric initial bifurcation paths, the bending load–deflection explicit relation is obtained by the two-step perturbation method again. A combination of two-step perturbation and modified Lindstedt–Poincare method is developed to obtain the approximate analytical solution of the strongly nonlinear forced vibration. Parameter investigations are conducted to discuss the different size-dependent effects, flow velocity and material distributions on the nonlinear behaviors. Results reveal the dual influences of structural size-dependent effects and indicate that the response is more sensitive to the size-dependent effects when the flow velocity is close to the critical buckling velocity.