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Research Papers

Vibrations of Pipes and Their Supporting Beams Caused by Tank Bulging Mode

[+] Author and Article Information
M. Utsumi

Machine Element Department,
Technical Research Laboratory,
IHI Corporation,
1 Shinnakaharacho, Isogo-ku, Yokohama,
Kanagawa Prefecture 235-8501, Japan

K. Ishida

Plant Engineering Operations,
IHI Corporation,
1-1, Toyosu 3-chome, Koto-ku,
Tokyo 135-8710, Japan

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 25, 2012; final manuscript received November 26, 2012; published online March 28, 2013. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 135(3), 031008 (Mar 28, 2013) (11 pages) Paper No: VIB-12-1118; doi: 10.1115/1.4023145 History: Received April 25, 2012; Revised November 26, 2012

The vibrations of pipes and their supporting beams caused by the tank bulging mode are analyzed. A computationally efficient semianalytical approach is presented by introducing a local velocity potential for each pipe and developing a reduced order model for the frame structure consisting of the pipes and their supporting beams. To enable the analysis, the system of governing equations and boundary conditions is derived in a variational form. Numerical results show that large bending stress occurs in the supporting beams attached to the lower part of the tank wall. This bending stress can be reduced by decreasing the outer diameter of the supporting beams based on the fact that the dependence of the bulging-mode-induced displacements of the supporting beams on their stiffness is weak. This stress reduction method does not increase but decreases the stiffness of the supporting beams and therefore the cost, unlike many methods for improving structural reliability. A method for reducing the axial compressive stress in the supporting beams is also investigated.

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Figures

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Fig. 1

Computational model

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Fig. 2

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

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Fig. 3

Frame structure consisting of pipes, connecting beams (c), and supporting beams (s)

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Fig. 4

Global displacement components (u¯,v¯,w¯) and local displacement components (u,v,w) of tank shell element ij

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Fig. 5

Tank and pipe displacements in the fifth mode (cosϕ-mode). (a) Radial displacement w¯|ϕ=0 of tank. (b) X- and Y-directional displacements uX1 and uY1 of pipe 1. (c) X- and Y-directional displacements uX2 and uY2 of pipe 2.

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Fig. 6

Tank and pipe displacements in the sixth mode (sinϕ-mode). (a) Circumferential displacement v¯|ϕ=0 of tank. (b) X- and Y-directional displacements uX1 and uY1 of pipe 1. (c) X- and Y-directional displacements uX2 and uY2 of pipe 2.

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Fig. 7

Time history of X-directional displacement uX1 of pipe 1 (Z = 32 m)

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Fig. 8

Responses at t = 1.97 s, at which they reach their maximum values in Fig. 7; (a) dynamic pressure -ρf∂φ/∂t|r=a,ϕ=0, (b) radial displacement w¯|ϕ=0 of tank, (c) X-directional displacements uX1 and uX2 (uX1 = uX2) of pipes 1 and 2

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Fig. 9

Bending stresses σ1=-Eby∂2uX1/∂Z2 and σ2=-Eby∂2uX2/∂Z2 (σ1=σ2) of pipes 1 and 2 (t = 1.97 s)

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Fig. 10

(a) Displacements and (b) bending stresses of supporting beams (t = 1.97 s)

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Fig. 11

(a) Displacement and (b) bending stress of supporting beam 2-16 at Z = 2.5 m (t = 1.97 s)

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Fig. 12

(a) Displacement and (b) bending stress of supporting beam 2-16 at Z = 2.5 m (t = 1.97 s)

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Fig. 13

Geometry of supporting beams at Z = 32 m

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Fig. 14

Axial stresses of supporting beams 6-23 and 6-24 (t = 1.97 s) (a) without three connecting beams and (b) with three connecting beams

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Fig. 15

Axial stresses of supporting beams 4-19 and 4-20 (t = 1.97 s) (a) without three connecting beams and (b) with three connecting beams

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