0
Research Papers

Dynamic Stability of Periodic Pipes Conveying Fluid

[+] Author and Article Information
Dianlong Yu

Laboratory of Science and Technology on
Integrated Logistics Support,
National University of Defense Technology,
Changsha Hunan 410073, China
Department of Mechanical Engineering,
McGill University,
Montreal, Québec H3A OC3, Canada
e-mail: dianlongyu@yahoo.com.cn

Michael P. Païdoussis

Department of Mechanical Engineering,
McGill University,
Montreal, Québec, Canada H3A OC3

Huijie Shen

Laboratory of Science and Technology on
Integrated Logistics Support,
National University of Defense Technology,
Changsha Hunan 410073, China
Department of Mechanical Engineering,
McGill University,
Montreal, Québec H3A OC3, Canada

Lin Wang

Department of Mechanics,
Huazhong University of Science & Technology,
Wuhan Hubei 430074, China

1Correspondence author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 8, 2013; final manuscript received April 28, 2013; accepted manuscript posted May 7, 2013; published online August 22, 2013. Assoc. Editor: Kenji Takizawa.

J. Appl. Mech 81(1), 011008 (Aug 22, 2013) (8 pages) Paper No: JAM-13-1012; doi: 10.1115/1.4024409 History: Received January 08, 2013; Revised April 28, 2013; Accepted May 07, 2013

In this paper, the stability of a periodic cantilevered pipe conveying fluid is studied theoretically by means of a novel transfer matrix method. This method is first validated by comparing the results to those available in the literature for a uniform pipe, showing that it is capable of high accuracy and displaying good convergence characteristics. Then, the stability of periodic pipes is investigated, with geometric, material-properties periodicity, and a combination of the two, showing that a considerable stabilizing effect may be achieved over different ranges of the mass parameter β (β=mf/(mf+mp), where mf and mp are the fluid and pipe masses per unit length). The effect of other different system parameters is also probed.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Topics: Stability , Pipes , Fluids
Your Session has timed out. Please sign back in to continue.

References

Chen, S. S., 1987, Flow-Induced Vibration of Circular Cylindrical Structures, Hemisphere, Washington, DC.
Païdoussis, M. P., and Li, G. X., 1993, “Pipes Conveying Fluid: A Model Dynamical Problem,” J. Fluids Struct., 7(2), pp. 137–204. [CrossRef]
Païdoussis, M. P., 1998, Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 1, Academic, London.
Païdoussis, M. P., 2004, Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 2, Elsevier, London.
Païdoussis, M. P., 2008, “The Canonical Problem of the Fluid-Conveying Pipe and Radiation of the Knowledge Gained to Other Dynamics Problems Across Applied Mechanics,” J. Sound Vib., 310(3), pp. 462–492. [CrossRef]
Païdoussis, M. P., 1993, “Some Curiosity-Driven Research in Fluid Structure Interactions and Its Current Applications,” ASME J. Pressure Vessel Technol., 115, pp. 2–14. [CrossRef]
Païdoussis, M. P., 2010, “The Dynamics of Cylindrical Conduits Containing Flowing Fluid,” 10th International Conference on Computational Structures Technology and 7th International Conference on Engineering Computational Technology, Valencia, Spain, September 14–17, B. H. V.Topping, J. M.Adam, F. J.Pallarés, R.Bru, and M. L.Romero, eds., Civil-Comp Press, Stirlingshire, UK.
Gregory, R. W., and Païdoussis, M. P., 1966, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid. I. Theory,” Proc. R. Soc. London, Ser. A, 293(1435), pp. 512–527. [CrossRef]
Gregory, R. W., and Païdoussis, M. P., 1966, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid. II. Experiments,” Proc. R. Soc. London, Ser. A., 293(1435), pp. 528–542. [CrossRef]
Guo, C. Q., Zhang, C. H., and Païdoussis, M. P., 2010, “Modification of Equation of Motion of Fluid-Conveying Pipe for Laminar and Turbulent Flow Profiles,” J. Fluids Struct., 26(5), pp. 793–803. [CrossRef]
Giacobbi, D. B., Rinaldi, S., Semler, C., and Païdoussis, M. P., 2012, “The Dynamics of a Cantilevered Pipe Aspirating Fluid Studied by Experimental, Numerical and Analytical Methods,” J. Fluids Struct., 30, pp. 73–96. [CrossRef]
Ghayesh, M. H., Païdoussis, M. P., and Modarres-Sadeghi, Y., 2011, “Three-Dimensional Dynamics of a Fluid-Conveying Cantilevered Pipe Fitted With an Additional Spring-Support and an End-Mass,” J. Sound Vib., 330(12), pp. 2869–2899. [CrossRef]
Vassilev, V. M., and Djondjorov, P. A., 2006, “Dynamic Stability of Viscoelastic Pipes on Elastic Foundations of Variable Modulus,” J. Sound Vib., 297(1), pp. 414–419. [CrossRef]
Doaré, O., and de Langre, E., 2002, “Local and Global Instability of Fluid-Conveying Pipes on Elastic Foundations,” J. Fluids Struct., 16(1), pp. 1–14. [CrossRef]
Doaré, O., 2010, “Dissipation Effect on Local and Global Stability of Fluid-Conveying Pipes,” J. Sound Vib., 329(1), pp. 72–83. [CrossRef]
Mead, D. J., 1996, “Wave Propagation in Continuous Periodic Structures: Research Contributions From Southampton, 1964–1995,” J. Sound Vib., 190(3), pp. 495–524. [CrossRef]
Aldraihem, O. J., and Baz, A., 2002, “Dynamic Stability of Stepped Beams Under Moving Loads,” J. Sound Vib., 250(5), pp. 835–848. [CrossRef]
Aldraihem, O. J., and Baz, A. M., 2004, “Moving-Loads-Induced Instability in Stepped Tubes,” J. Vibr. Control, 10(1), pp. 3–23. [CrossRef]
Ruzzene, M., and Baz, A., 2006, “Dynamic Stability of Periodic Shells With Moving Loads,” J. Sound Vib., 296(296), pp. 830–844. [CrossRef]
Shen, H. J., Wen, J. H., Yu, D. L., and Wen, X. S., 2009, “The Vibrational Properties of a Periodic Composite Pipe in 3D Space,” J. Sound Vib., 328(1–2), pp. 57–70. [CrossRef]
Yu, D. L., Wen, J. H., Zhao, H. G., Liu, Y. Z., and Wen, X. S., 2008, “Vibration Reduction by Using the Idea of Phononic Crystals in a Pipe-Conveying Fluid,” J. Sound Vib., 318(1–2), pp. 193–205. [CrossRef]
Sorokin, S., 2012, “On Power Flow Suppression in Straight Elastic Pipes by Use of Equally Spaced Eccentric Inertial Attachments,” ASME J. Vibr. Acoust., 134, p. 041003. [CrossRef]
Wen, J. H., Shen, H. J., Yu, D. L., and Wen, X. S., 2010, “Theoretical and Experimental Investigation of Flexural Wave Propagating in a Periodic Pipe With Fluid-Filled Loading,” Chin. Phys. Lett., 27(11), p. 114301. [CrossRef]
Yu, D. L., Wen, J. H., Zhao, H. G., Liu, Y. Z., and Wen, X. S., 2011, “Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory,” ASME J. Vibr. Acoust., 133(1), p. 014502. [CrossRef]
Marzani, A., Mazzotti, M., Viola, E., Vittori, P., and Elishakoff, I., 2012, “FEM Formulation for Dynamic Instability of Fluid-Conveying Pipe on Nonuniform Elastic Foundation,” Mech. Based Des. Struct. Mach., 40(1), pp. 83–95. [CrossRef]
Huang, Y., Zeng, G., and Wei, F., 2002, “A New Matrix Method for Solving Vibration and Stability of Curved Pipes Conveying Fluid,” J. Sound Vib., 251(2), pp. 215–225. [CrossRef]
Ma, X. Q., Xiang, Y., and Huang, Y. Y., 2004, “A Transfer Matrix Method for Solving Stability of Pipes Conveying Fluid on Elastic Foundation With Various End Supports,” Eng. Mech., 21(4), pp. 194–198 (in Chinese).
Ryu, S. U., Sugiyama, Y., and Ryu, B. J., 2002, “Eigenvalue Branches and Modes for Flutter of Cantilevered Pipes Conveying Fluid,” Comput. Struct., 80(14), pp. 1231–1241. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Sketch of a binary periodic pipe, (b) one cell with segments A and B, (c) the segment B with nB subsegments

Grahic Jump Location
Fig. 2

Stability curves for the uniform pipe: (a) the dimensionless critical flow velocity uc as a function of β; (b) the dimensionless critical frequency ωc as a function of β. The circle (○), square (□) and triangle (△) curves correspond to the number of segments A and B, nA = nB = 1, 10 and 100, respectively. The arrows in Fig. 2(a) show the location of the jumps.

Grahic Jump Location
Fig. 3

The stability curves for a geometrically periodic pipe. The circle (○) and square (□) curves correspond to the periodic and the uniform pipe, respectively.

Grahic Jump Location
Fig. 4

The stability curves for different outer radius of segment A. The circle (○), square (□), and triangle (△) thick curves and dot (•) thin curve correspond to outer radii of 0.08 m, 0.07 m, 0.06 m, and a uniform pipe, respectively.

Grahic Jump Location
Fig. 5

The stability curves for different values of the lattice constant, a. The circle (○), square (□), and triangle (△) curves correspond to a equal to 1 m, 2 m, and 5 m, respectively.

Grahic Jump Location
Fig. 6

The stability curves for different length ratio, η. The circle (○), square (□), and triangle (△) curves are correspond to η equal to 1/3, 1, and 2, respectively.

Grahic Jump Location
Fig. 7

The stability curves for the material-periodic pipe. The circle (○) and square (□) curves are illustrated as the periodic and the uniform pipe.

Grahic Jump Location
Fig. 8

The stability curves for different material for segment A. The circle (○), square (□), and triangle (△) curves correspond to the material as lead, steel and aluminum, respectively.

Grahic Jump Location
Fig. 9

The stability curves for combination periodic pipe. The circle (○), square (□), and triangle (△) curves correspond to the material periodic, geometrical periodic and combination periodic pipe, respectively.

Tables

Errata

Discussions

Related

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In