Dynamic Stability of a Slightly Curved Viscoelastic Pipe Conveying Fluid

  • K. O. Orolu Department of Systems Engineering, University of Lagos, Nigeria
  • T. A. Fashanu Department of Systems Engineering, University of Lagos, Nigeria
  • A. A. Oyediran Department of Mechanical Engineering, University of Lagos, Lagos, Nigeria
Keywords: bifurcation; critical velocity; initial curvature; vibration; viscoelastic


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.


Chen L., Yang X. (2005), Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models, International Journal of Solids and Structures (42) 37–50.
Djondjorov, P. (2001). Dynamic stability of pipes partly resting on Winkler foundation. Journal of Theoretical and Applied Mechanics, 31(3): 101-112.
Doare O. (2010), Dissipation effect on local and global stability of fluid-conveying pipes, Journal of Sound and Vibration (329) 72–83
Dodds, H. L., and Runyan, H. L. (1965). Effect of High-Velocity Fluid Flow on the Bending Vibrations and Static Divergence of a Simply Supported Pipe. Report No. NASA-TN-2870.
Feng, Z. Y., Wang, Z. M., & Zhao, F. Q. (2004). Dynamic Stability Of Kelvin Viscoelastic Pipes Conveying Fluid With Both Ends Simply Supported. Engineering Mechanics, 1, 033.
Holmes, P. J., (1977), “Bifurcations to Divergence and Flutter in Flow-Induced Oscillations: A Finite Dimensional Analysis,” J. Sound Vib., 53(4), 471–503.
Ibrahim, R. A. (2010). Overview of Mechanics of Pipes Conveying Fluids — Part I : Fundamental Studies, Journal of Pressure Vessel Technology. Transaction of the (132):1–32.
Li, Y. D., & Yang, Y. R. (2017). Nonlinear vibration of slightly curved pipe with conveying pulsating fluid. Nonlinear Dynamics, 88(4), 2513-2529.
Orolu, K. O., Fashanu, T. A., & Oyediran, A. A. (2019). Cusp bifurcation of slightly curved tensioned pipe conveying hot pressurized fluid. Journal of Vibration and Control, 25(5), 1109-1121.
Owoseni, O. D., Orolu, K. O., & Oyediran, A. A. (2018). Dynamics of slightly curved pipe conveying hot pressurized fluid resting on linear and nonlinear viscoelastic foundations. Journal of Vibration and Acoustics, 140(2), 021005.
ÖZ, H. R., and Boyaci, H., (2000), “Transverse Vibration of Tensioned Pipes Conveying Fluid With Time-Dependent Velocity,” J. Sound Vib., 236(2), 259–276
Özhan B. B., Pakdemirli M.(2013), Effect of Viscoelasticity on the natural frequency of Axially Moving Continua, Advances in Mechanical Engineering, 1-7
Paidoussis, M.P., (2014). Fluid-Structure Interactions: Slender Structures and Axial Flow, vol. 1. Academic Press, London.
Qiao, N., and Huang, Y.,(2001). Dynamic Analysis of Restrained Viscoelastic Pipe Conveying Fluid, Journal of Huazhong University of Science and Technology, 29(2), 87-89.
Qiao, N., Zhang, H. I., Huang, Y. Y., and Chen, Y. P.,(2000), Differential Quadrature Method for the Stability Analysis of Semi-Circular Pipe Conveying Fluid With Spring Support, Journal of Engineering Mechanics, 17(6) 59–64.
Sinir, B. G. (2010). Bifurcation and Chaos of Slightly Curved Pipes, Mathematical and Computational Applications 15(3), 490–502.
Vassilev, V. M., and Djondjorov, P. A., (2006), Dynamic Stability of Viscoelastic Pipes on Elastic Foundations of Variable Modulus, Journal of Sound Vibration,1(2) 414–419
Wang L., Dai H. L., Qian Q.,(2012) Dynamics of Simply Supported fluid Conveying pipes with geometric imperfections, Journal of Fluids and Structures, (29)97-106
Yang, X., Yang, T., & Jin, J. (2007). Dynamic stability of a beam-model viscoelastic pipe for conveying pulsative fluid. Acta Mechanica Solida Sinica, 20(4), 350-356.
Zhao F., Wang Z., Feng Z., Liu H.(2001) Stability analysis of Maxwell viscoelastic pipes Conveying fluid with both ends simply supported, Applied Mathematics and Mechanics 22(12) 1436-1445
How to Cite
Orolu, K. O., Fashanu, T. A., & Oyediran, A. A. (2020). Dynamic Stability of a Slightly Curved Viscoelastic Pipe Conveying Fluid. Journal of Engineering Research, 24(1), 1-10. Retrieved from http://jer.unilag.edu.ng/article/view/586