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–Poincaré 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.

流体输送纳米管是纳米机电系统中的重要组件，需要严格的静态和动态刚度设计。研究了在屈曲前和屈曲后状态下流体输送功能梯度纳米管的非线性弯曲和受迫振动。基于张福的精细位移场，建立了一个综合的尺寸相关纳米管模型，其中非局部应力、应变梯度和表面能效应在构造模型中耦合。假定纳米管在两端简单支撑并承受横向均匀静态或谐波载荷。扩展了两步扰动技术以获得屈曲后平衡路径，为弯曲和共振分析提供初始配置。根据两条对称的初始分岔路径，弯曲载荷-挠度显式关系再次通过两步微扰法得到。开发了两步微扰和改进的 Lindstedt-Poincaré 方法的组合，以获得强非线性受迫振动的近似解析解。进行参数研究以讨论不同尺寸相关的影响、流速和材料分布对非线性行为的影响。结果揭示了结构尺寸相关效应的双重影响，并表明当流速接近临界屈曲速度时，响应对尺寸相关效应更为敏感。开发了两步微扰和改进的 Lindstedt-Poincaré 方法的组合，以获得强非线性受迫振动的近似解析解。进行参数研究以讨论不同尺寸相关的影响、流速和材料分布对非线性行为的影响。结果揭示了结构尺寸相关效应的双重影响，并表明当流速接近临界屈曲速度时，响应对尺寸相关效应更为敏感。开发了两步微扰和改进的 Lindstedt-Poincaré 方法的组合，以获得强非线性受迫振动的近似解析解。进行参数研究以讨论不同尺寸相关的影响、流速和材料分布对非线性行为的影响。结果揭示了结构尺寸相关效应的双重影响，并表明当流速接近临界屈曲速度时，响应对尺寸相关效应更为敏感。