Dynamics of axially functionally graded pipes conveying fluid using a higher order shear deformation theory

Abstract

This study presents a novel approach for addressing dynamical characteristics of fluid conveyingaxially functionally graded pipes. The variation of material properties of the pipe along axialdirection is taken into account according to a power-law function. Owing to a unified expressionfor displacement field, the developed model can be recast into classical Euler – Bernoulli andTimoshenko tube models as well as a newly developed higher order shear deformable tube model;the latter satisfies zero-shear conditions on free surfaces, and hence yields more realistic results.The system of partial differential equations governing dynamics of fluid conveying axiallyfunctionally graded pipes is derived through utilization of Hamilton’s principle. Differentialquadrature scheme is used to discretize the system of differential equations and generate numericalresults. Detailed numerical investigations of the current fluid-solid interaction problem elucidatethe effects of material gradation pattern, transverse shear deformation distribution profile alongradial direction and fluid velocity on the natural frequencies of fluid conveying functionally gradedpipes. The critical fluid velocity, which is a significant design parameter, can also be determinedby means of developed procedures in this study.