On stability of a slightly curved Maxwell viscoelastic pipe conveying fluid resting on linear viscoelastic foundation

ABSTRACT

Viscoelastic pipes are commonly found in various industry applications. When undergoing deformations, a viscoelastic material combines both viscous and elastic behaviours, by exhibiting time-dependent strains. Hamilton’s principle is employed to derive the governing equation for the slightly curved viscoelastic pipe resting on an elastic medium. The pipe’s viscoelasticity is assumed using the Maxwell model. Three trigonometric function are used to describe the initial curvatures, while Eigenfunction expansion method was used to convert the partial differential equation to a set of four ODE’s in time. The Eigenvalues, corresponding to the natural frequencies, were obtained up to four modes. Numerical results show the influence of the initial curvature, viscoelastic coefficient and the linear elastic medium on the frequency and fluid velocity of the pipe. It is noticeable that the initial curvature and the elastic medium cause the bifurcations point of the slightly curved pipe to be extended. For low viscoelasticity coefficient, the results obtained show two dissimilar imaginary frequencies. This is unlike what is previously reported in the literature. For higher coefficient, the pipe behaves like a steel pipe. At higher velocities, coupled mode flutter are absent for some modes depending on the boundary condition.

KEYWORDS:

• Maxwell model
• fluid conveying pipes
• natural frequency
• slightly curved pipe
• Eigenfunction expansion

Additional information

Notes on contributors

Akintoye O. Oyelade

Akintoye O. Oyelade obtained his B.Sc., M.Sc., in Civil Engineering from University of Lagos, Nigeria. He obtained his PhD in the Department of Mechanics in the school of Aerospace Engineering at Beijing Institute of Technology, Beijing, China in 2018. He is a lecturer and researcher in the Department of Civil and Environmental Engineering, University of Lagos, Nigeria. His research interest is in mechanics, acoustic, waves, and vibration of structures.

Osamudiamen G. Ikhile

Osamudiamen G. Ikhile obtained his Bachelor of Engineering in Agricultural Engineering at University of Ilorin in 2009. He completed his Master of Science at University of Lagos in 2020. He is currently working with Zakhem Construction Nigeria.

Ayo A. Oyediran

Ayo Oyediran obtained a First Class in Mechanical Engineering from University of Lagos in June 1977. He proceeded to the Department of Theoretical and Applied Mechanics at Cornell in September 1979. He worked with G. S. S. Ludford on Unsteady Detonations. He graduated with a PhD in Applied Mechanics in Jan 1985. Worked at NASA in the US for about 15 years on various projects including Jet Noise, Combustion Acoustics Instabilities, Microgravity Fluid flows to name a few. He is presently with the Department of Mechanical Engineering at the University of Lagos. His research interests include Double Diffusive of Heat and Mass Transfer Natural Convection, Flow induced vibrations of offshore pipes and pipelines.