0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Eisinger, F. L., 1997, “Designing Piping Systems Against Acoustically Induced Structural Fatigue,” J. Pressure Vessel Technol., 119, pp. 379–383. [CrossRef]
Eisinger, F. L., and Francis, J. T., 1999, “Acoustically Induced Structural Fatigue of Piping Systems,” J. Pressure Vessel Technol., 121, pp. 438–443. [CrossRef]
Eisinger, F. L., and Sullivan, R. E., 2007, “Acoustic Resonance in a Package Boiler and Its Solution—A Case Study,” J. Pressure Vessel Technol., 129, pp. 759–762. [CrossRef]
American Petroleum Institute, 1995, API Standard 618, Reciprocating Compressors for Petroleum, Chemical and Gas Industry Services.
Moussou, P., Vaugrante, P., Guivarch, M., and Seligmann, D., 2000, “Coupling Effects in a Two Elbows Piping System,” Flow-Induced Vibrations, S.Ziada and T.Staubli, eds., Balkema, Rotterdam, pp. 579–586.
Ohayon, R., 2004, “Reduced Models for Fluid–Structure Interaction Problems,” Int. J. Numer. methods Eng., 60, pp. 139–152. [CrossRef]
Moussou, P., 2005, “A Kinematic Method for the Computation of Natural Modes of Fluid-Structure Interaction Systems,” J. Fluids Struct., 20, pp. 643–658. [CrossRef]
Ginsberg, J. H., 2010, “On Dowell's Simplification for Acoustic Cavity-Structure Interaction and Consistent Alternatives,” J. Acoust. Soc. Am., 127, pp. 22–32. [CrossRef] [PubMed]
Goyder, H., 2007, “Acoustic-Structural Coupling in Pipework,” Proceedings of ASME Pressure Vessel and Piping Division Conference, No. ASME PVP 2007-26200.
Goyder, H., 2008, “Simple Equations for Acoustic-Structural Coupling,” Proceedings of the 9th International Conference on Flow-Induced Vibrations, Prague.
Bendat, J. S., and Piersol, A. G., 1986, Random Data-Analysis and Measurement Procedures, 2nd ed., Wiley-Interscience, NY.
Au-Yang, M. K., 2001, Flow-Induced Vibration of Power and Process Plant Components, 1st ed., ASME Press, New York.
Pierce, A. D., 1981, Acoustics: An Introduction to Its Physical Principles and Applications, McGraw-Hill Book Company, New York.
Kinsler, L. E., Frey, A. R., Coppens, A. B., and Sanders, J. V., 2000, Fundamentals of Acoustics, Wiley and Sons, NY.
Gibert, R. J., 1988, Vibrations des Structures–Interactions Avec les Fluides – Sources d‘Excitation Aleatoires, Eyrolles, Paris (in French).
Axisa, F., and Antunes, J., 2007, Modelling of Mechanical Systems: Fluid-Structure Interaction, Elsevier, NY.
Lamb, H., 1932, Hydrodynamics, Dover, NY.
Meirovitch, L., 1967, Analytical Methods in Vibrations, The MacMillan Company, NY.
Weaver, D. S., Ziada, S., Au-Yang, M. K., Chen, S. S., Paidoussis, M. P., and Pettigrew, M. J., 2000, “Flow-Induced Vibration of Power and Process Plant Components: Progress and Prospects,” ASME J. Pressure Vessel Technol., 122, pp. 339–348. [CrossRef]
Lafon, P., Caillaud, S., Devos, J., and Lambert, C., 2003, “Aeroacoustical Coupling in a Ducted Shallow Cavity and Fluid/Structure Effects on a Steam Line,” J. Fluids Struct., 18, pp. 695–713. [CrossRef]
Mace, B. R., and Manconi, E., 2008, “Modelling Wave Propagation in Two-Dimensional Structures Using Finite Element Analysis,” J. Sound Vib., 318, pp. 884–902. [CrossRef]
Fuller, C. R., and Fahy, F. J., 1982, “Characteristics of Wave Propagation and Energy Distributions in Cylindrical Elastic Shells Filled With Fluids,” J. Sound Vib., 81, pp. 501–518. [CrossRef]
DeJong, C. A. F., 1994, “Analysis of Pulsations and Vibrations in Fluid-Filled Pipe Systems,” Ph.D. thesis, Eindhoven University of Technology, Delft, The Netherlands.
Fahy, F., 1985, Sound and Structural Vibration–Radiation, Transmission and Response, Academic Press, NY.
Kaneko, S., NakamuraT., 2008, Flow-Induced Vibrations, Classifications and Lessons From Practical Experiences, Elsevier, NY.
Nayyar, M. L., 1973, Piping Handbook, McGraw-Hill, NY.
Moussou, P., Lafon, P., Potapov, S., Paulhiac, L., and Tijsseling, A. S., 2004, “Industrial Cases of FSI Due to Internal Flows,” Proceedings of the 9th International Conference on Pressure Surges, Chester, UK, The BHR Group.
Moussou, P., 2006, “An Attempt to Scale the Vibrations of Water Pipes,” J. Pressure Vessel Technol., 128, pp. 670–676. [CrossRef]
Morse, P. M., and Ingard, K. U., 1968, Theoretical Acoustics, McGraw-Hill, NY.
Morand, H., and Ohayon, R., 1995, Fluid-Structure Interaction, Applied Numerical Methods, Wiley, NY.
Landau, E. D., and Lifchitz, E. D., 1987, Theory of Elasticity, Elsevier, NY.
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, McGraw-Hill, NY.
Vernon, J. B., 1967, Linear Vibration Theory, Wiley and Sons, NY.
Blevins, R. D., 1984, Formulas for Natural Frequency and Mode Shape, Krieger.
Païdoussis, M. P., 2006, Fluid-Structure Interactions–Slender Structure and Axial Flows, Vol. 2, Elsevier, NY.
Flügge, W., 1960, Stresses in Shells, Springer, Berlin.
Abramowitz, M., and Stegun, I. A., 1965, Handbook of Mathematical Functions, Dover, NY.

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. 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)

Grahic Jump Location
Fig. 3

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

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. 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.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In