Stability Analysis of Fluid Conveying Axially Functionally Graded Micro-Pipes Using a Refined Tube Model

Abstract

The aim of the current study is to put forward a new model for stability analysis of axially functionally graded micro-pipes conveying fluid. Modified couple stress theory is employed to capture the scale effects. The displacement field is presented in a unified form such that the formulations based on conventional Euler-Bernoulli and Timoshenko theories as well as newly developed higher order shear deformable tube model which properly satisfies transverse shear requirements on free surfaces, are retrievable. The material properties are assumed to be varying through-the-length according to a power-law function. Hamilton's principle is utilized to derive formulation governing the current fluid-solid interaction problem. In order to generate numerical results, the system of equations is discretized and converted to the standard generalized eigenvalue problem by utilizing differential quadrature technique. The influences of size which is captured by length scale parameter of modified couple stress theory, material distribution pattern, geometrical aspects, and fluid velocity upon the stability of axially functionally graded micro-pipes conveying fluid have been elucidated through detailed numerical investigations. Developed procedures also enable determination of the value of critical flow velocity, which is a significant parameter in designing small-scale pipes containing internal flow.