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Research Papers

Nonplanar Vibration of a Vertical Fluid-Conveying Pipe (Effect of Horizontal Excitation at the Upper End)

[+] Author and Article Information
Kiyotaka Yamashita

Professor
Department of Mechanical Engineering,
Fukui University of Technology,
3-6-1, Gakuen,
Fukui, Fukui 910-8505, Japan
e-mail: yamashita@fukui-ut.ac.jp

Hiroaki Furuya

Department of Mechanical Engineering,
Keio University,
3-14-1, Hiyoshi, Kouhoku,
Yokohama, Kanagawa 223-8522, Japan
e-mail: fhgyj735@yahoo.co.jp

Hiroshi Yabuno

Professor
Graduate School of Systems
and Information Engineering,
University of Tsukuba,
1-1-1, Ten-no-dai,
Tsukuba Science,
Ibaraki 305-8573, Japan
e-mail: yabuno@esys.tsukuba.ac.jp

Masatsugu Yoshizawa

Professor Emeritus
Department of Mechanical Engineering,
Keio University,
3-14-1, Hiyoshi, Kouhoku,
Yokohama, Kanagawa 223-8522, Japan
e-mail: ypeko@jcom.home.ne.jp

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 5, 2012; final manuscript received April 5, 2014; published online April 29, 2014. Assoc. Editor: Walter Lacarbonara.

J. Vib. Acoust 136(4), 041005 (Apr 29, 2014) (12 pages) Paper No: VIB-12-1339; doi: 10.1115/1.4027401 History: Received December 05, 2012; Revised April 05, 2014

Nonlinear and nonplanar lateral vibration of a self-excited vertical cantilevered pipe conveying fluid is studied for the case that the upper end of the pipe is periodically excited in the horizontal direction. The modulation equations, which are coupled with nonlinear terms and govern the amplitudes and phases of nonplanar vibration, are analytically derived. When the excitation frequency is near the nonplanar limit cycle frequency, the nonplanar self-excited vibration is quenched to the excitation, and the amplitude of lateral vibration in the direction perpendicular to the horizontal excitation is decreased. Experiments were conducted and spatial pipe behaviors were observed using two CCD cameras. The theoretically predicted effects of horizontal excitation were confirmed qualitatively.

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References

Figures

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Fig. 1

Nonplanar vibration of a fluid-conveying pipe with horizontal external excitation

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Fig. 2

Complex eigenvalue λv as a function of flow velocity V for the lowest three modes (α = 0.13, β = 0.24, γ = 20.6)

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Fig. 3

Bifurcation diagram for self-excited nonplanar pipe vibration with no horizontal excitation: (a) steady-state amplitude of nonplanar pipe vibration hs; (b) comparison of nonlinear frequency ωnp of self-excited nonplanar pipe vibration with natural frequency ωr

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Fig. 4

Nonplanar self-excited pipe vibration with no horizontal excitation (V = 6.0): (a) transient time histories of a and b; (b) transient time history of Ω; and (c) steady-state nonplanar motion at s = 0.7

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Fig. 5

Bifurcation diagram for nonplanar pipe vibration with horizontal external excitation (PL, NP, κ = 0.0077, V = Vcr = 5.68): (a) steady-state amplitude as; (b) steady-state amplitude bs

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Fig. 6

Bifurcation diagram for nonplanar pipe vibration with horizontal external excitation (PL, NP, κ = 0.0077, V = 6.0): (a) steady-state amplitude as; (b) steady-state amplitude bs; (c) steady-state phase difference ηs; (d) steady-state phase difference Ωs. (Region A) planar motion; (region B) nonplanar beat motion; (region C) elliptic nonplanar motion; (region D) elliptic nonplanar motion or planar motion; and (region E) elliptic nonplanar motion

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Fig 7

Stability boundaries of the amplitude hp in frequency quenching on the σ–V plane under horizontal external excitation

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Fig. 8

Planar motion in frequency quenching under horizontal external excitation (σ = 0, κ = 0.0077, V = 6.0): (a) transient time histories of a and b; (b) transient time history of η

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Fig. 9

Pipe motion in a horizontal plane at s = 0.7 with horizontal external excitation (κ = 0.0077, V = 6.0): (a) and (b) nonplanar beat motion in region B; (c) planar motion in frequency quenching in region A; (d) elliptic motion in frequency quenching in region C; (e) planar motion in frequency quenching in region D; and (f) nonplanar beat motion in region E

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Fig. 10

Experimental setup

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Fig. 11

Measurement system

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Fig. 12

Nonplanar self-excited pipe vibration with no horizontal excitation (vs = 5.9 m/s, s = 0.7, experiment): (a) time histories of v and w in a steady-state; (b) nonplanar motion

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Fig. 13

Planar pipe motion in frequency quenching under horizontal external excitation (N/2π = 2.0 Hz, vs = 5.9 m/s, s = 0.7, experiment): (a) time histories of v, w, and Y0, their spectrum analyses; (b) pipe motion in the horizontal plane including excitation direction

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Fig. 14

Elliptic pipe motion in frequency quenching under horizontal external excitation (N/2π = 2.15 Hz, vs = 5.9 m/s, s = 0.7, experiment): (a) time histories of v, w, and Y0, their spectrum analyses; (b) elliptic nonplanar motion

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Fig. 15

Pipe motion in the horizontal plane with horizontal external excitation (vs = 5.9 m/s, s = 0.7, experiment): (a) nonplanar beat motion (N/2π = 1.85 Hz); (b) nonplanar beat motion (N/2π = 2.3 Hz)

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