Non-trivial equilibriums and natural frequencies of a slightly curved pipe conveying supercritical fluid

Abstract

Despite extensive use of curved pipes conveying high-speed fluids in many engineering fields, few researches have been conducted on the supercritical dynamics of curved pipes to explore new dynamic behavior. For the first time, this paper investigates the vibration characteristics of a slightly curved pipe conveying fluids in a supercritical range. The generalized Hamilton's principle is adopted to derive the governing equation. The non-trivial equilibriums and the critical flow velocities are then analytically obtained. The analytical predictions agree well with the numerical results obtained using the finite difference method and the differential quadrature element method. By introducing the coordinate transformation, the governing equation of the curved pipe is established for the vibration about the non-trivial equilibrium position. The natural frequencies of the pipe are obtained by the Galerkin truncation method and verified with the discrete Fourier transform. It is found that the critical velocities and the natural frequencies are highly dependent on the initial curvature. The research results show an interesting phenomenon that the natural frequency of the curved pipe may increase as the pipe length increases, but may not in monotonous manner. The obtained results provide useful information for further studies of fluid-conveying pipes with geometric imperfection.