Stability analysis of viscoelastic pipes conveying fluid with different boundary conditions described by fractional Zener model

Abstract

The stability of viscoelastic pipes conveying fluid with the Zener fractional-order constitutive relationship is investigated in this paper. The pipe is subjected to the axial follower and directed forces with uniform distribution. The pipe’s beginning and end are restrained with lateral and rotational springs to satisfy a vast range of boundary conditions. The fluid flow effect is taken into account as a lateral distributed force. Based on the Euler-Bernoulli beam theory, the equation of motion is derived using the extended Hamilton’s principle. The Laplace transform and Galerkin method are used to obtain a set of algebraic equation. The pipe conveying fluid’s stability boundary will be obtained by calculating the roots of the determinant of the obtained equations coefficients. Effects of the fractional Zener viscoelastic model parameters are considered on the stability margin of pipes conveying fluid with different boundary conditions, and some conclusions are drawn.