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Research Papers: Technical Forum

On the Coincidence of the Acoustical and Mechanical Natural Frequencies of a Pressure Vessel

[+] Author and Article Information
Pierre Moussou

Laboratoire de Mecanique des Structures Industrielles Durables,
Unite Mixte de Recherche CNRS EDF CEA 8193,
1, Avenue du General de Gaulle,
91912 Clamart Cedex, France
e-mail: pierre.moussou@edf.fr

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 16, 2012; final manuscript received February 19, 2013; published online May 21, 2013. Assoc. Editor: Njuki W. Mureithi.

J. Pressure Vessel Technol 135(3), 030902 (May 21, 2013) (9 pages) Paper No: PVT-12-1059; doi: 10.1115/1.4024014 History: Received May 16, 2012; Revised February 19, 2013

A widespread conception among field engineers is that the coincidence of the structure and of the acoustic frequencies of a pressure vessel triggers a dramatic increase in the vibration level, leading to fatigue failure. The physics of fluid-structure interaction are revisited in order to clarify this effect, and a simple model of inertial coupling is proposed on the basis of one structure mode and one acoustic mode. It is shown that even if the uncoupled natural frequencies coincide, the coupled frequencies are split apart by an amount depending on the ratio of the fluid density and of the structure density, and on the spatial correlation of the fluid field. As a consequence, a large increase of the vibration level is more likely to occur in a gas system than in a liquid system. Illustrations based on dispersion equations are provided for cylindrical structures filled with vapor and water.

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Figures

Grahic Jump Location
Fig. 1

Modulus of the transfer function defined by Eq. (6) for different values of the coupling coefficient ηc (⋆:10-4,Δ:0.05,•:0.2,+:0.5) and of the uncoupled frequencies ratio (upper figure: 5, middle figure: 2, lower figure: 1)

Grahic Jump Location
Fig. 4

Dispersion curves for a steel cylinder filled with low pressure vapor. Upper plot: n = 2, lower plot: n = 3.

Grahic Jump Location
Fig. 2

Modulus of the transfer function defined by Eq. (7) for different values of the coupling coefficient ηc (⋆:10-4,Δ:0.05,•:0.2,+:0.5) and of the modal damping coefficient (upper figure: 2×10-3, middle figure: 10-2, lower figure: 5×10-2)

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Fig. 3

Example of a three lobed mode shape for a side branch (left) and for a vertical tank (right)

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Fig. 5

Zoom on the dispersion curves for a steel cylinder filled with low pressure vapor. Upper plot: n = 2, lower plot: n = 3. Plain line: coupled branch, dashed line: structure branch with incompressible fluid, dotted line: acoustic branch.

Grahic Jump Location
Fig. 6

Dispersion curves for a steel cylinder filled with high pressure vapor. Upper plot: n = 2, lower plot: n = 3.

Grahic Jump Location
Fig. 7

Zoom on the dispersion curves for a steel cylinder filled with high pressure vapor. Upper plot: n = 2, lower plot: n = 3. Plain line: coupled branch, dashed line: structure branch with incompressible fluid, dotted line: acoustic branch.

Grahic Jump Location
Fig. 8

Dispersion curves for a thin steel cylinder filled with water. Upper plot: n = 2, lower plot: n = 3. Plain line: coupled branch, dashed line: structure branch with incompressible fluid, dotted line: acoustic branch.

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