Nonlinear Dynamic Analysis of FG Fluid Conveying Micropipes with Initial Imperfections

This paper investigates the nonlinear dynamics of FG-FCMPs with initial imperfections. Based on the MCST, the nonlinear equations of motion and the corresponding boundary conditions are established by applying Hamilton’s principle, the Euler–Bernoulli beam theory, and von-Kármán geometric nonlinearity. To describe the initial geometric imperfection of the FG-FCMP, the first-order vibrational mode is employed. Subsequently, in cases of primary parametric resonance, 1:2 subharmonic resonance for the first-order mode, as well as primary resonance for the second-order mode, Galerkin’s method, and the multiple scale method are utilized to analyze the amplitude–frequency responses of the imperfect FG-FCMP. The numerical simulations test the influence of flow velocity, micro-scale parameter, geometrical imperfections, and external loads on the nonlinear characteristics of a coupled system with two DOFs. It is found that, as the increase of flow velocity, micro-scale effect, and external load, the amplitude of the first two modes can be increased. The hardening characteristics are converted into the softening characteristics due to the imperfect effect. Furthermore, numerical results provide a more comprehensive understanding of the nonlinear dynamics of FCMPs for both periodic and chaotic motions.