Concerning the Effect of a Viscoelastic Foundation on the Dynamic Stability of a Pipeline System Conveying an Incompressible Fluid

Document Type: Research Paper

Authors

1 Department of Systems Engineering, Faculty of Engineering, University of Lagos

2 Centre for Space Transport and Propulsion, National Space Research and Development Agency

3 Department of Mechanical & Biomedical Engineering, College of Engineering, Bells University of Technology

Abstract

In this paper, we present an analytical method for solving a well-posed boundary value problem of mathematical physics governing the vibration characteristics of an internal flow propelled fluid-structure interaction where the pipeline segment is idealized as an elastic hollow beam conveying an incompressible fluid on a viscoelastic foundation. The effect of Coriolis and damping forces on the overall dynamic response of the system is investigated. In actuality, for a pipe segment supported at both ends and subject to a free motion, these two forces generate conjugate complex frequencies for all flow velocities. On employing integral transforms and complex variable functions, a closed form analytical expression is derived for the overall dynamic response. It is demonstrated that a concise mathematical expression for the natural frequency associated with any mode of vibration can be deduced from the algebraic product of the complex frequency pairs. By a way of comparative analysis for damping decrement physics reminiscent with laminated structures, mathematical expressions are derived to illustrate viscoelastic damping effects on dynamic stability for any flow velocity. The integrity of the analytical solution is verified and validated by confirming theresults in literature in appropriate asymptotic limits.

Keywords

Main Subjects

[1] Paidoussis, M.P. (2013) Fluid-structure interactions: slender structures and axial flows, Vol. 1, Academic Press, Revised Edition.

[2] 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, 1:59-74.

[3] Paidoussis, M.P. &Issid, N.T. (1974) Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration 33, 267-294.

[4] Murai, M. and Yamamoto, M. (2010) An Experimental Analysis of the Internal Flow Effects on Marine      Risers. Proceedings of MARTEC 2010, P.159-165.

[5] Marakala N, Appukutttan K.K, and Kadoli R. (2014) Experimental and Theoretical Investigation of Combined Effects of Fluid and Thermal Induced Vibration on Vertical Thin Slender Tube. IOSR- JMCE, ISSN: 2278-1684, pp: 63-68.

[6] Ziegler, H.  (1968) Principles of Structural Stability. Waltham, MA: Blaisdell.

[7] 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.

[8] Stein, R.A., Tobriner, M.W. (1970) Vibration of pipes containing flowing fluids. Trans ASME J Appl. Mechanics; 906-916.

[9] Dermendjian-Ivanova, D.S. (1992) Critical flow velocities of a simply supported pipeline on an    elastic foundation. J Sound Vibration; 157: 370-374.

[10] Chary, S.R., Rao, C.K., Iyengar, R.N. (1993) Vibration of Fluid Conveying Pipe on Winkler Foundation, Proceedings of the 8th National Convention of Aerospace Engineers on Aeroelasticity, Hydroelasticity and other Fluid-Structure Interaction Problems, IIT Kharagpur, India; pp. 266-287.

[11] Doaré, O., de Langre, O. (2002) Local and global instability of fluid conveying pipes on elastic foundation. J Fluids &Structures; 16: 1-14.

[12] Chellapilla, K.R. and Simha, H.S. (2008) Vibrations of Fluid-Conveying Pipes Resting on Two-Parameter Foundation. The Open Acoustics Journal, 1, 24-33.

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

[14] Saxena, A. and Patel, R.K. (2013) Vibration Control of Cantilever Beam Using Eddy Current Damper. International Journal of Engineering and Innovative Technology (IJESIT) Volume 2, Issue 3.

[15] Jae-ung, B., Moon, K.K. and Daniel, J.I. (2005) Vibration Suppression of a Cantilever Beam   Using Eddy Current Damper. Journal of Sound and Vibration 284, 805-824.

[16] Tonoli, A. (2007) Dynamic characteristics of Eddy current dampers and couplers. Journal of Sound and Vibration 301: 576-591.

[17] Olayiwola, P.S. (2016) Mechanics of a Fluid-Conveying Pipeline System Resting on a Viscoelastic Foundation. Journal of Multidisciplinary Engineering Science Studies (JMESS), ISSN: 2458-925X Vol. 2. Issue 3.

[18] Szmidt T and Przybylowicz P. (2013) Critical Flow Velocity with Electromagnetic Actuators. Journal of Theoretical and Applied Mechanics 51, 2, pp. 487-496.

[19] Kuye, S.I. (2013) Analysis of the Dynamics of Offshore Fluid-Conveying Viscoelastic Pipes Resting on a Deformable Sea Bed. Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 4(5): 742-751.

[20] Jeffrey A. (2002) Advanced Engineering Mathematics, Harcourt Academic Press. U.S.A, p.596.

[21] Wrede, R. C. and Spiegel, M. (2002) Thoery and Problems of Advanced Calculus 2nd Ed. Schaum’s Outline Serises, McGraw-Hill, p. 364.

[22] Nash, W. A. (1977) Thoery and Problems of Strength of Materials, 2nd Ed. Schaum’s Outline Series, McGraw-Hill, p. 83, 159-161.

[23] Cole E.B. (1960) Theory of Vibrations. The University of Liverpool.

[24] Darkov, A. (1983) Structural Mechanics. Mir Publishers, Moscow.