Dynamics of axially functionally graded pipes conveying fluid

Pipes conveying fluid near jet engines or rocket engines always subject to gradient temperature, which results in the gradient Young's modulus. The influence of the Young's modulus gradient on dynamics of pipes conveying fluid is studied for the first time. The pipe is treated as an axially functional gradient (AFG) Euler-Bernoulli beam. By using the generalized Hamilton's principle, the nonlinear partial-differential-integral governing equation of the AFG pipe conveying fluid with simply supported boundaries is established. On the basis of it, the effects of gradient Young's modulus on the natural characteristics and the non-trivial equilibrium configuration are analyzed. To simulate the pipe directly, the differential quadrature element method (DQEM) is introduced. The harmonic balance method is carried out to solve the response analytically. In the supercritical region, the non-trivial equilibrium configuration is superposed by modal shapes of a simply supported Euler-Bernoulli beam and verified by the DQEM. The results show that the gradually varied Young's modulus along the axial direction leads to the asymmetric non-trivial equilibrium configuration. An increasing gradient of Young's modulus can raise the critical fluid velocity of the buckled system and weaken the vibration. Unlike the pipe in the subcritical region, the pipe in the supercritical region will generate zero shift to the response. At the same time, the pipe changes the hard characteristic to the soft one, and the non-trivial equilibrium configuration introduces more resonance peaks to the system. The results also show that under the same external excitation, the increasing Young's modulus gradient will strengthen the nonlinearity of the response and further enlarge the asymmetry of the vibration shape. This work further complements the theory of pipes conveying fluid.