Nonlinear vibration and instability of functionally graded nanopipes with initial imperfection conveying fluid

Abstract

• A fluid-conveying FG nanopipe model associated with the initial imperfection is developed. • Nonlinear vibration and instability behaviors of the FG nanopipe are studied. • Size-dependent behaviors of the FG nanopipe are captured by nonlocal strain gradient theory. • Influence of system parameters on the critical velocity and frequency of the FG nanopipe is examined. In this paper, the nonlinear vibration and instability of a fluid-conveying nanopipe made of functionally graded (FG) materials with consideration of the initial geometric imperfection are investigated. The material properties are assumed to vary smoothly along the radial direction according to a power-law exponent form. The fluid-conveying FG nanopipe is modeled as a Euler-Bernoulli beam, and the governing equation is derived based on the nonlocal strain gradient theory incorporating the effects of Von-Karman geometrical nonlinearity and initial imperfection. The nonlinear frequency and critical fluid velocity are achieved via He's Hamiltonian approach. After verifying the present model with comparison of several previous studies, the effect of several different system parameters including the amplitude of the nonlinear oscillator, the initial geometric imperfection, size-dependent parameters, and the power-law index on the frequency response of the fluid-conveying FG nanopipe are explored. Moreover, the critical velocity of the conveying fluid under different system parameters is also investigated and discussed in detail. The developed size-dependent nonlinear model is expected to provide a possible theoretical way to guide the application of FG nanopipe as micro/nanofluidic devices.