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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.

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Copyright © 2014 by ASME
Topics: Stability , Pipes , Fluids
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References

Figures

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Fig. 1

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

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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.

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Fig. 3

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

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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.

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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.

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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.

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Fig. 7

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

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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.

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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.

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