International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Nawras Haidar Mostafa*

 Mechanical Engineering Department, College of Engineering, University of Babylon, Babel, Iraq


 

Download Citation: |
Download PDF


ABSTRACT


In this study, the natural frequency of a simply supported pipeline (hinged type) conveying one-dimension incompressible steady fluid flow set on viscoelastic foundation is investigated by using finite element analysis and the critical fluid velocity with different parameters such as stiffness and viscous coefficients of foundation are obtained. The foundation is simulated using the modified Winkler's model to introduce the effect of time dependent viscosity term. Some known results are confirmed and some new ones obtained. Two components of foundation, stiffness and viscosity, seemed to act on the critical flow velocity of the pipe in contrary trend. Where, increasing the foundation stiffness tended to increase the critical flow velocity in the pipe. While, increasing foundation viscosity attempted to decrease it. At some ranges of pipe length, the foundation viscosity effect seems to be more extreme. Increasing the fluid velocity leads to monotonic reduction in the system damping ratio. Two parameters, pipe length and fluid density which relate to the natural frequency of pipeline conveying fluid are studied in detail and the results indicate that the effect of Coriolis force on natural frequency is become more effective by increasing pipe length and fluid density besides increasing fluid flow velocity. 


Keywords: Finite element; fluid-structural interaction; modified Winkler model; viscoelastic foundation; simply supported pipe; stability.


Share this article with your colleagues

 


REFERENCES


[1] Bourrieres, F. J. 1939. “Sur Un Phenomene D’oscillation Auto-Entretenue En Mecanique Des Fluids Reels”. Publications Scientifiques et Techniques du Ministere de L’Air, (147). French.

[2] Lottati, I. and Kornecki, A. 1986 .The effect of an elastic foundation and of dissipative forces on the stability of fluid conveying pipes. Journal of Sound and Vibration, 109(2): 327-338.

[3] Chen, H. 1991. “Vibration of a Pipeline Containing Fluid Flow with Elastic Support”. M. Sc. Thesis, Ohio University.

[4] Lee, S. Y. and Mote, C. D. 1997. A generalized treatment of the energetics of translating continua, part II: beams and fluid conveying pipes. Journal of Sound and Vibration, 204(5): 735-753.

[5] Elishakoff, I. and Impolonia, N. 2001. Does a partial elastic foundation increase the flutter velocity of a pipe conveying fluid? Journal of Applied Mechanics-Transactions of the ASME, 68(2): 206-212.

[6] Djondjorov, P. 2001. Dynamic stability of pipes partly resting on winkler foundation. Journal of Theoretical and Applied Mechanics, 31(3): 101-112.

[7] Djondjorov, P., Vassilev, V., and Dzhupanov, V. 2001. Dynamic stability of fluid conveying cantilevered pipes on elastic foundations. Journal of Sound and Vibration, 247(3): 537-546.

[8] Djondjorov, P. 2001. On the critical velocities of pipes on variable elastic foundation. Journal of Theoretical and Applied Mechanics, 31(4): 73-81.

[9] Païdoussis, M. P. 2004. “Fluid-Structure Interactions”. Vol. 2. Academic Press: London.

[10] Lumijärvi, J. 2006. “Optimization of Critical Flow Velocity in Cantilevered Fluid Conveying Pipes, with a Subsequent Non-Linear Analysis”. Academic Dissertation to be presented with the assent of the Faculty of Technology, FI-90014 University of Oulu, Finland.

[11] Huang, Y., Liu, Y., Li, B., Li, Y., and Yue, Z. 2010. Natural frequency analysis of fluid conveying pipeline with different boundary conditions. Nuclear Engineering and Design, 240(3): 461-467.

[12] Mahrenholtz, O. H. 2010. Beam on viscoelastic foundation: an extension of Winkler’s model. Archive of Applied Mechanics, 80(1): 93-102.

[13] Thomsen, J. and Dahl, J. 2010. Analytical predictions for vibration phase shifts along fluid-conveying pipes due to Coriolis forces and imperfections. Journal of Sound and Vibration, 329(15): 3065-3081.

[14] Rinaldi, S., Prabhakar, S., Vengallatore, S., and Michael, P. 2010. Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability. Journal of Sound and Vibration, 329, 8: 1081-1088.

[15] Païdoussi, M. P. 1998. “Fluid-Structure Interactions, Slender Structures and Axial Flow. Volume One, Academic Press: California, USA.

[16] Benjamin, T. B. 1961. Dynamics of a system of articulated pipes conveying fluid: theory. (a). Proceedings of the Royal Society (London) A, 261, 1307: 457-486.

[17] Benjamin, T. B. 1961. Dynamics of a system of articulated pipes conveying fluid. (b). Proceedings of the Royal Society (London) A, 261, 1307: 487-499.

[18] Rao, S. S. 2004. “The Finite Element Method in Engineering”. 4th ed. Elsevier Science & Technology Books.

[19] Caughey, T. K. and O'Kelly, E. J. 1961. Effect of damping on the natural frequencies of linear dynamic systems. Journal of the Acoustical Society of America, 33, 11: 1458-1461.

[20] Beards, C. F. 1996. “Structural Vibration: Analysis and Damping”. 1st ed. Butterworth-Heinemann: An imprint of Elsevier Science.

[21] Krodkiewski, J. M., 2008. “Mechanical Vibrations”. 1st ed. The University of Melbourne, Department of Mechanical and Manufacturing Engineering: Melbourne.

[22] Doared, O. and De Langre, E. 2002. Local and global instability of fluid-conveying pipes on elastic foundations. Journal of Fluids and Structures, 16(1): 1-14.


ARTICLE INFORMATION


Received: 2013-05-29
Revised: 2013-11-02
Accepted: 2013-11-21
Available Online: 2014-03-01


Cite this article:

Mostafa, N.H. 2014. Effect of a viscoelastic foundation on the dynamic stability of a fluid conveying pipe. International Journal of Applied Science and Engineering, 12, 59–74. https://doi.org/10.6703/IJASE.2014.12(1).59