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Research Papers: Seismic Engineering

Beating in Pipes Subject to Shock

[+] Author and Article Information
Rudolph J. Scavuzzo

Consultant,
Hi-Test Laboratories,
Arvonia, VA 23004
e-mail: rscrud@aol.com

Domenic Urzillo

NSWCCD,
Philadelphia, PA 19112-1403
e-mail: domenic.urzillo@navy.mil

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received February 14, 2014; final manuscript received October 11, 2014; published online December 17, 2014. Assoc. Editor: Chong-Shien Tsai.

J. Pressure Vessel Technol 137(2), 021801 (Apr 01, 2015) (5 pages) Paper No: PVT-14-1026; doi: 10.1115/1.4028839 History: Received February 14, 2014; Revised October 11, 2014; Online December 17, 2014

Often when a pipe is subjected to a shock input in the vertical direction, the pipe will vibrate horizontally after initially vibrating vertically. This vibration is beating that occurs between the vertical and horizontal modes of the pipe. Beating vibration was examined analytically by considering the principal directions of the moment of inertia of the pipe with respect to the shock input direction and by varying the support direction and stiffness at each end of a pipe. Both the moment of inertia and piping supports can produce beating. The conditions needed to initiate this phenomenon are examined and results presented. Two pipe configurations are examined: a cantilever pipe and a pipe supported at each end. In both cases, the effects of varying the principal directions of the moment inertia were examined. The end conditions were varied in the supported pipe. In one case, similar vertical and horizontal supports were specified and in the second two cases vertical supports with two different stiffnesses were analyzed. Beating was found when the end supports were in different directions

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References

Figures

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Fig. 1

Mode 1 vertical direction (XY plane) 32.11 Hz

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Fig. 2

Mode 2 horizontal direction (XZ plane) 32.42 Hz. Mode 2 is identical to mode 1 but in a different plane.

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Fig. 3

Mode 3 vertical direction (XY plane) 194.3 Hz

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Fig. 4

Mode 4 horizontal direction (XZ plane) 196.1 Hz. Mode 4 is identical to mode 3 but different plane.

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Fig. 5

Model used for the dynamic response of a cantilever beam with Ixy = 0 and Ixy 0.5 in4. The end of element 1 is fixed.

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Fig. 6

Dynamic response of a cantilever pipe with Ixy = 0

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Fig. 7

Dynamic response of a cantilever pipe with Ixy = 0.5 in4. Beating between the vertical and horizontal modes of vibration occurs.

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Fig. 8

FEA model that have with end supports inline but with different stiffnesses. The lengths of the right-hand supports (+X) are about one half of the left-hand supports. Two cases were analyzed: Ixy = 0 (case 1) and Ixy = 0.5 in4 (case 3).

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Fig. 9

Response of the pipe with inline supports of different stiffnesses and Ixy = 0 (case 1)

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Fig. 10

FEA model that have with end supports rotated 90 deg with identical stiffnesses, Ixy = 0 (case 2)

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Fig. 11

Response of the pipe with identical supports at 90 deg from each other and Ixy = 0 (case 2)

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Fig. 12

Beating response of the pipe with inline supports of different stiffnesses and Ixy = 0.5 in4. (case 3)

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