Stability optimization of spinning FGM pipes conveying fluid via intermediate elastic supports

This paper aims to the optimal design of intermediate elastic supports in spinning functionally graded material (FGM) pipes conveying fluid for maximum critical velocity. Employing Hamilton's principle, the governing equations of spinning pipes conveying fluid with intermediate elastic supports are derived based on the Timoshenko beam theory. With the help of the Laplace transform method, the exact frequency equations and closedform modal functions of multi-span spinning FGM pipes with any number of intermediate elastic supports or any number of intermediate simple supports are obtained, and the reliability of the methods in this paper is verified. Through numerical examples, the effects of intermediate supports, boundary conditions, flow velocity, and power law exponent on stability characteristics and critical flow velocity are discussed. Taking two-span and three-span systems as examples, the optimal positions and critical stiffness of the supports are obtained, and the maximum principle of critical velocity of multi-span spinning pipe is found. Through this maximum principle, the maximum critical flow velocity of the multi-span system can be conveniently estimated by the high-order instability flow velocities of the single-span system. The work of this paper has positive significance for dynamic analysis and optimization design of pipe-conveying fluid systems.