Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans

Abstract

In this paper, a dynamical model of spinning multi-span pipes conveying fluid is proposed and the transverse natural and resonant frequencies and mode characteristics of such system are explored. The pipe body is considered to be composed of functionally graded materials (FGMs), in which a power law is used to govern the distribution of material properties along the pipe wall thickness. The partial differential equations (PDEs) governing two transverse motions of the pipe are derived by the extended Hamilton principle, in which the contributions of the FGM and intermediate supports are highlighted. The PDEs are discretized by the Galerkin procedure and the eigensystem theorem is applied to find the numerical solutions. The results show that various frequency characteristics can be attainable by use of different materials and mixing patterns. Attachments of intermediate supports can heighten the rigidity and improve the stability of spinning FG pipes conveying fluid, which are consequently used as “stabilizers” for the slender drill strings. Also, the mode characteristics of different spans will determine the locations of vibration amplitude of the pipes.