Document Type : Research Paper


Mechanical Engineering Department, University of Technology -Iraq, Alsina’a street, 10066 Baghdad, Iraq.


The investigation of the vibration of pipes containing flowing fluid is very essential to obtain an understanding of their dynamic behavior and prevent their catastrophic failure due to fatigue. Pipelines are subjected to environmental static and dynamic loading including self-weight, restoring, and Carioles forces. This research aims to investigate the vibrations of pipeline structures for examining their structural integrity under these conditions. A linear Euler-Bernoulli beam model is used to analyze the dynamic response of flexible, inclined, and fixed ends pipe conveying fluid made of polypropylene random-copolymer. Closed-form expression for dynamic response is presented by using combining of finite Fourier sine and Laplace transforms method. The influences of the inclination angle, thermal load, and aspect ratio (ratio of outside diameter to the length of pipe) on the dynamical behavior of the pipe–fluid system are studied. The obtained results attest to the importance of considering combining effects of the inclination angle, thermal load, and aspect ratio in analyzing and designing pipe conveying fluid. It is observed that the dynamic deflection can be significantly increased by increasing temperature, aspect ratio, and fluid velocity, while it reduced by increasing the inclination angle with the horizontal axis in the range of (0-90).


  • Temperature variation, inclination angle, and aspect ratio have strongly affected on vibration characteristics of pipe-fluid system.
  • Thermal effects in the pipe are very important factor and more significant in comparison with the internal fluid velocity.
  • Inclination angle has larger impact on vibration characteristics at higher aspect ratio.


Main Subjects

[1] Michael Paidoussis, Fluid-Structure Interactions: Slender Structures and Axial Flow, Elsevier Academic Press, London, (2004).
[2] R. Askarian, M. R. Permoon, and M. Shakouri, Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions, International Journal of Mechanical Sciences, 179, pp. 1-10, August (2020).
[3] R. Khodabakhsh, A. R. Saidi, and R. Bahaadini, An analytical solution for nonlinear vibration and post-buckling of functionally graded pipes conveying fluid considering the rotary inertia and shear deformation effects, Applied Ocean Research, 101 (2020) 1-17.
[4] G. W. Housner, Bending vibration of a pipe line containing flowing fluid, Journal of Applied Mechanics, 19 (1952) 205-208.
[5] R. A. Stein, and M. W. Tobriner, Vibration of Pipes Containing Flowing Fluids, Journal of Applied Mechanics, 37(1970) 906-916.
[6] D. S. Weaver, and T. E. Unny, On the Dynamic Stability of Fluid- Conveying Pipes, Journal of Applied Mechanics, 40 (1975) 48-52.
[7] R. H. Plaut, and K. Huseyin, Instability of Fluid-Conveying Pipes under Axial Load, Journal of Applied Mechanics, 42 (1975) 889-890.
[8] F. J. Hatfield, D. C. Wiggert, R. S. Otwell, Fluid Structure Interaction in Piping by Component Synthesis, Journal of Applied Mechanics, 104 (1982) 318-325.
[9] M. W. Lesmez, D. C. Wigge, and F. J., Hatfield, Modal Analysis of Vibrations in Liquid-Filled Piping Systems, Journal of Fluids Engineering, 112 (1990) 311-318.
[10] M. J. Jweeg, and Z. I. Mohammad, Vibration Characteristics of Different Cross-Section Pipes with Different End Conditions, Engineering and Technology Journal28 (2010) 1634-1654.
[11] Z. Lu, K. Zhang, H. Ding, and L. Chen, Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials, Nonlinear Dynamics, 100 (2020) 1091–1104.
[12] Y. Amini, M. Heshmati, F. Daneshmand, Dynamic behavior of conveying-fluid pipes with variable wall thickness through circumferential and axial directions, Marine Structures, 72 (2020) 1-18.
[13] D.B. Giacobbi, C. Semler, and M.P. Païdoussis, Dynamics of pipes conveying fluid of axially varying density, Journal of Sound and Vibration, 473 (2020) 1-10.
[14] J. ElNajjar, and F. Daneshmand, Stability of horizontal and vertical pipes conveying fluid under the effects of additional point masses and springs, Ocean Engineering, 206 (2020).
[15] R. A. Ibrahim, Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies, Journal of Pressure Vessel Technology, 132 (2010) 034001-1-034001-32.
[16] Y. Dianlong, M. P. Païdoussis, H. Shen, and L. Wang, Dynamic Stability of Periodic Pipes Conveying Fluid, Journal of Applied Mechanics, 81 (2014) 011008-1-011008-8.
[17] N. Haidar, S. Obaid, and M. Jawad, Instability of Angled Pipeline Arising from Internal Fluids Flow, The Iraqi Journal for Mechanical and Material Engineering, 12 (2012) 222-237.
[18] J. H. Mohmmed, M. A. Tawfik, Q. A. Atiyah, Natural Frequency and Critical Velocities of Heated Inclined Pinned PP-R Pipe Conveying Fluid, journal of achievements in materials and manufacturing engineering, 107 (2021) 15-27.
[19] M. P. Paidousiss, and G. li, Pipes Conveying Fluid: A Model Dynamical Problem. Journal of Fluids and Structures. 7 (1993) 137-204.
[20] Q. Ni, Z. L. Zhang, and L. Wang, Application of the differential transformation method to vibration analysis of pipes conveying fluid, Applied Mathematics and Computation, 217 (2011) 7028-7038.
[21] R. S. Reddy, S. Panda, and A. Gupta, Nonlinear dynamics of an inclined FG pipe conveying pulsatile hot fluid, International Journal of Non-Linear Mechanics, 118 (2020) 1-15.
[22] J. Wu, Dynamic analysis of an inclined beam due to moving loads, Journal of Sound and Vibration, 288 (2005) 107–131.
[23] A. Mamandi, and M. H. Kargarnovin, Dynamic analysis of an inclined Timoshenko beam traveled by successive moving masses/forces with inclusion of geometric nonlinearities, Act Mechanical, 218 (2011) 9–29.
[24] A. Mamandi, M. H. Kargarnovin, and D. Younesian, Nonlinear dynamics of an inclined beam subjected to a moving load, Nonlinear Dynamics, 60 (2010) 277–293.