Technical Brief

Vibration Analysis of Pipes Supported by a Flexible Tank Wall Considering the Support Clearances

[+] Author and Article Information
M. Utsumi

Technical Research Laboratory,
Machine Element Department,
IHI Corporation,
1 Shinnakaharacho,
Isogo-ku, Yokohama,
Kanagawa Prefecture 235-8501, Japan
e-mail: masahiko_utsumi@ihi.co.jp

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 25, 2016; final manuscript received September 14, 2016; published online October 27, 2016. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 139(1), 014501 (Oct 27, 2016) (10 pages) Paper No: VIB-16-1144; doi: 10.1115/1.4034778 History: Received March 25, 2016; Revised September 14, 2016

The vibration of pipes supported by a flexible tank wall is analyzed taking into account the hydroelastic vibration of the tank and the nonlinearity caused by the support clearances. Because the support clearances increase the pipe displacement, it is important to examine whether the support clearances augment the pipe stress. We illustrate that the support clearances can cause an increase in the pipe stress not only due to the increase in pipe displacement but also to the difference between elastic behaviors of the tank wall and pipes. The tank wall and pipes are dominated by membrane and bending deformations, respectively. Furthermore, we illustrate that the support clearances render a stress reduction method ineffective. In this study, a semi-analytical method is applied, rather than a full finite element analysis. The semianalytical method is helpful not only for computationally efficient analysis but also for gaining physical insight into the clearance-nonlinearity-induced stress behaviors noted above.

Copyright © 2017 by ASME
Topics: Pipes , Displacement , Stress
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Fig. 1

Analysis model and tank-fixed coordinates

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Fig. 2

Local cylindrical coordinates (ri,φi,Z) for each pipe

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Fig. 3

Frame structure consisting of pipes, connecting beams (c), and supporting beams (s) (at each pipe support, different numbers are assigned to the ends of pipe member and supporting beam)

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Fig. 4

Support clearance between member ends 4 and 17 shown in Fig. 3 (R and θ are coordinates fixed to the ring)

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Fig. 5

Relative displacement Urel of pipe to ring

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Fig. 6

Mode shapes for case without clearances (coupling between displacements of pipe and tank wall is present, eigenfrequency is 2.54 Hz)

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Fig. 7

Mode shapes for case with clearances. (a) Eigenmode in which coupling between displacements of pipe and tank wall is present (eigenfrequency 2.54 Hz). (b) Eigenmode in which pipe displacement is prevailing (eigenfrequency 3.08 Hz).

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Fig. 8

Responses of U4X, U17X, and Uex in case with clearances (in the case without clearances, U4X and U17X are almost the same as U17X shown in this figure)

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Fig. 9

Displacement of pipe 1 in X direction and displacement of tank wall in r direction at φ = 0 (t = 1.97 s)

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Fig. 10

Bending stress in pipe 1 (t = 1.97 s)

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Fig. 11

Displacement of pipe 1 in X direction and displacement of tank wall in r direction at φ = 0 (t = 1.32 s, the case for a smaller liquid depth h = 20 m)

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Fig. 12

Bending stress in pipe 1 (t = 1.32 s, the case for a smaller liquid depth h = 20 m)

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Fig. 13

Bending stress of supporting beam 15–22 (t = 1.97 s). (a) Case with clearances and (b) case without clearances.

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Fig. 14

Displacement of supporting beam 15–22 (t = 1.97 s). (a) Case with clearances and (b) case without clearances.

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Fig. 15

A model used to compare the approaches corresponding to the present analysis and the conventional idea

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Fig. 16

Eigenfrequency of the system shown in Fig. 15; ρf = 1000 kg/m3, L = 20 m, h1 = 0.01 m, h2 = 0.04 m, (a) b1 = 1 m, b2 = 1.6 m, and (b) b1 = 0.2 m, b2 = 1.6 m; (curves represent results based on the present analysis and conventional idea, that are in agreement)

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Fig. 17

Convergence of K1(λnri)/K1(λnai) (Eq. (B1)) with increasing ri/ai (h = 35 m, ai = 0.305 m)




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