Dynamic Stability of a Slightly Curved Viscoelastic Pipe Conveying Fluid

Abstract

It has been established both in theory and experiment that perfectly straight pipe is an idealisation that does not exist in practice. Viscoelastic pipes are commonly used in various industrial applications. When undergoing deformations, a viscoelastic material combines both viscous and elastic behaviours, by exhibiting time-dependent strains. A few researchers have worked on slightly curved elastic pipes conveying fluid but most of the works have not considered slightly curved viscoelastic pipe. This work analyzes the effect of the viscoelastic property on a slightly curved pipe conveying fluid. The developed nonlinear partial differential equation (PDE) of motion is decomposed and converted to a system of nonlinear ordinary differential equations (ODE) using Eigen-function expansion method. The resulting ODE is then solved by the Runge Kutta 4th order method. The dynamical analysis of the pipe is presented using bifurcation diagrams and phase plane portraits. The results obtained show that viscoelastic property attenuates buckling instability of the pipe and the route to chaos is via periodic doubling.