Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature

Abstract

In the view of the dynamic behaviors of fluid-conveying pipes become more complex in the supercritical case that it is quite common in engineering, we concentrate on the supercritical fluid-conveying pipe composed of functionally graded material and study the nonlinear vibration for the first time to provide an insight reference for the possible applications of the practice pipe. Firstly, the nonlinear dynamic equations are deduced by Hamiltonian’s principle based on the Euler-Bernoulli and Timoshenko theories. Then the non-trivial equilibrium expressions and the critical fluid velocities are derived analytically for the straight pipe and pipe with initial curvature. For the straight FGM pipe, we conclude that the critical fluid velocity of the Euler-Bernoulli model is larger than that of the Timoshenko model. For the FGM pipe with initial curvature, it is shown that the equilibrium deformations of Euler–Bernoulli model are larger than those of Timoshenko model. For a larger initial curvature, the critical fluid velocity becomes smaller, and the bifurcation occurs earlier for both pipe models. Moreover, Galerkin method is used to analysis the frequencies of the supercritical fluid-conveying FGM Timoshenko pipes based on the buckling configuration. We obtain that the frequencies increase as the power-law exponent and initial tension increase.