Determination of Natural Frequency and Critical Velocity of Inclined Pipe Conveying Fluid under Thermal Effect by Using Integral Transform Technique
This study proposes an analytical solution of natural frequencies for an inclined fixed supported Euler-Bernoulli pipe containing the flowing fluid subjected to thermal loads. The integral transform technique is employed to obtain the spatial displacement-time domain response of the pipe-fluid system. Then, a closed-form analytical expression is presented. The effects of various geometric and system parameters on the vibration characteristics of pipe-fluid system with different flow velocities are discussed. The results illustrate that the proposed analytical solution agrees with the solutions achieved in previous works. The proposed model predicts that the pipe loses the stability by divergence with the increasing flow velocity. It is evident that the influences of inclination angle and temperature variation are dramatically increased at a higher aspect ratio. Additionally, it is demonstrated that the temperature variation becomes a more harmful effect than the internal fluid velocity on the stability of the pipe at elevated temperature.
M. P. Païdoussis, Fluid-Structure Interactions: Slender Structures and Axial Flow, 2nd ed., London: Academic Press, 2014.
V. Olunloyo, C. Osheku, and P. Olayiwola, “Concerning the Effect of a Viscoelastic Foundation on the Dynamic Stability of a Pipeline System Conveying an Incompressible Fluid,” Journal of Applied and Computational Mechanics, vol. 2, no. 2, pp. 96-117, 2016.
G. W. Housner, “Bending Vibration of a Pipe Line Containing Flowing Fluid,” Journal of Applied Mechanics, vol. 19, no. 2, pp. 205-208, June 1952.
R. A. Stein and M. W. Tobriner, “Vibration of Pipes Containing Flowing Fluids,” Journal of Applied Mechanics, vol. 37, no. 4, pp. 906-916, December 1970.
M. P. Païdoussis, “Flutter of Conservative Systems of Pipes Conveying Incompressible Fluid,” Journal of Mechanical Engineering Science, vol. 17, no. 1, pp. 19-25, February 1975.
R. H. Plaut and K. Huseyin, “Instability of Fluid-Conveying Pipes under Axial Load,” Journal of Applied Mechanics, vol. 42, no. 4, pp. 889-890, December 1975.
F. J. Hatfield, D. C. Wiggert, and R. S. Otwell, “Fluid Structure Interaction in Piping by Component Synthesis,” Journal of Applied Mechanics, vol. 104, no. 3, pp. 318-325, September 1982.
M. W. Lesmez, D. C. Wiggert, and F. J. Hatfield, “Modal Analysis of Vibrations in Liquid-Filled Piping Systems,” Journal of Fluids Engineering, vol. 112, no. 3, pp. 311-318, September 1990.
Q. Qian, L. Wang, and Q. Ni, “Instability of Simply Supported Pipes Conveying Fluid under Thermal Loads,” Mechanics Research Communications, vol. 36, no. 3, pp. 413-417, April 2009.
D. Zhao, J. Liu, and C. Q. Wu, “Stability and Local Bifurcation of Parameter-Excited Vibration of Pipes Conveying Pulsating Fluid under Thermal Loading,” Applied Mathematics and Mechanics, vol. 36, no. 8, pp. 1017-1032, August 2015.
J. K. Kukla, “Application of the Green Functions to the Problem of the Thermally Induced Vibration of a Beam,” Journal of Sound and Vibration, vol. 262, no. 4, pp. 865-876, May 2003.
J. R. Blandino and E. A. Thornton, “Thermally Induced Vibration of an Internally Heated Beam,” Journal of Vibration and Acoustics, vol. 123, no. 1, pp. 67-75, January 2001.
F. K. Alfosail, A. H. Nayfeh, and M. I. Younis, “Natural Frequencies and Mode Shapes of Statically Deformed Inclined Risers,” International Journal of Non-Linear Mechanics, vol. 94, pp. 12-19, September 2017.
C. Gan, S. Jing, S. Yang, and H. Lei, “Effects of Supported Angle on Stability and Dynamical Bifurcations of Cantilevered Pipe Conveying Fluid,” Applied Mathematics and Mechanics, vol. 36, no. 6, pp. 729-746, May 2015.
D. S. Yang and C. M. Wang, “Dynamic Response and Stability of an Inclined Euler Beam under a Moving Vertical Concentrated Load,” Engineering Structures, vol. 186, pp. 243-254, May 2019.
B. Ram, Engineering Mathematics, India: Pearson Education, 2009.
X. Liang, Z. Wu, L. Wang, G. Liu, Z. Wang, and W. Zhang, “Semianalytical Three-Dimensional Solutions for the Transient Response of Functionally Graded Material Rectangular Plates,” Journal of Engineering Mechanics, vol. 141, no. 9, pp. 1-17, September 2015.
Y. D. Li and Y. R. Yang, “Forced Vibration of Pipe Conveying Fluid by the Green Function Method,” Archive of Applied Mechanics, vol. 84, no. 12, pp. 1811-1823, July 2014.
H. B. Wen, Y. R. Yang, P. Li, Y. D. Li, and Y. Huang, “A New Method Based on Laplace Transform and Its Application to Stability of Pipe Conveying Fluid,” Shock and Vibration, vol. 2017, 1472601, 2017.
Z. Lai, L. Jiang, and W. Zhou, “An Analytical Study on Dynamic Response of Multiple Simply Supported Beam System Subjected to Moving Loads,” Shock and Vibration, vol. 2018, 2149251, 2018.
X. Tan, H. Ding, and L. Q. Chen, “Nonlinear Frequencies and Forced Responses of Pipes Conveying Fluid via a Coupled Timoshenko Model,” Journal of Sound and Vibration, vol. 455, pp. 241-255, September 2019.
L. Jiang, Y. Zhang, Y. Feng, W. Zhou, and Z. Tan, “Dynamic Response Analysis of a Simply Supported Double-Beam System under Successive Moving Loads,” Applied Sciences, vol. 9, no. 10, 2162, May 2019.
W. T. Thomson, Theory of Vibration with Applications, London: Unwin Hyman, 1988.
M. Ali, I. Alshalal, and J. H. Mohmmed, “Effect of the Torsional Vibration Depending on the Number of Cylinders in Reciprocating Engines,” International Journal of Dynamics and Control, vol. 9, pp. 901-909, January 2021.
J. H. Mohmmed, M. A. Tawfik, and 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, vol. 107, no. 1, pp. 15-27, 2021.
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, vol. 217, no. 16, pp. 7028-7038, April 2011.
X. Liang, X. Zha, X. Jiang, L. Wang, J. Leng, and Z. Cao, “Semi-Analytical Solution for Dynamic Behavior of a Fluid-Conveying Pipe with Different Boundary Conditions,” Ocean Engineering, vol. 163, pp. 183-190, September 2018.
A. O. Adelaja, “Natural Frequencies of Pressurized Hot Fluid Conveying Pipes,” FUOYE Journal of Engineering and Technology, vol. 3, no. 2, pp. 131-135, September 2018.
V. O. Olunloyo, C. A. Osheku, and P. S. Olayiwola, “A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System,” Advances in Acoustics and Vibration, vol. 2017, 8141523, 2017.
R. H. Plaut, “Postbuckling and Vibration of End-Supported Elastic Pipes Conveying Fluid and Columns under Follower Loads,” Journal of Sound and Vibration, vol. 289, no. 1-2, pp. 264-277, January 2006.
V. O. Olunloyo, C. A. Osheku, and S. I. Kuye, “Vibration and Stability Behaviour of Sandwiched Viscoelastic Pipes Conveying a Non-Newtonian Fluid,” 29th International Conference on Ocean, Offshore, and Arctic Engineering, pp. 99-111, June 2010.
H. Ashley and G. Haviland, “Bending Vibrations of a Pipe Line Containing Flowing Fluid,” Journal of Applied Mechanics, vol. 17, no. 3, pp. 229-232, September 1950.
K. O. Orolu, T. A. Fashanu, and A. A. Oyediran, “Cusp Bifurcation of Slightly Curved Tensioned Pipe Conveying Hot Pressurized Fluid,” Journal of Vibration and Control, vol. 25, no. 5, pp. 1109-1121, March 2019.
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