Fluid-Structure Interaction

Structural-Acoustic Vibration Problems in the Presence of Strong Coupling

[+] Author and Article Information
Heinrich Voss

e-mail: voss@tuhh.de

Markus Stammberger

e-mail: markus.stammberger@tuhh.de
Institute of Numerical Simulation
Hamburg University of Technology
D-21073 Hamburg, Germany

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received March 14, 2011; final manuscript received November 3, 2011; published online November 28, 2012. Assoc. Editor: Samir Ziada.

J. Pressure Vessel Technol 135(1), 011303 (Nov 28, 2012) (8 pages) Paper No: PVT-11-1082; doi: 10.1115/1.4007251 History: Received March 14, 2011; Revised November 03, 2011

Free vibrations of fluid–solid structures are governed by unsymmetric eigenvalue problems. A common approach which works fine for weakly coupled systems is to project the problem to a space spanned by modes of the uncoupled system. For strongly coupled systems, however, the approximation properties are not satisfactory. This paper reports on a framework for taking advantage of the structure of the unsymmetric eigenvalue problem allowing for a variational characterization of its eigenvalues and structure preserving iterative projection methods. We further cover an adjusted automated multilevel substructuring (AMLS) method for huge fluid–solid structures. The reliability and efficiency of the method are demonstrated by the free vibrations of a structure completely filled with water.

© 2013 by ASME
Topics: Fluids , Eigenvalues
Your Session has timed out. Please sign back in to continue.


Ginsberg, J., 2010, “Derivation of a Ritz Series Modeling Technique for Acoustic Cavity-Structural Systems Based on a Constrained Hamilton Principle,” J. Acoust. Soc. Am., 127, pp. 2749–2758. [CrossRef] [PubMed]
Morand, H. J.-P., and Ohayon, R., 1995, Fluid Structure Interaction (Applied Numerical Methods), John Wiley & Sons, Masson.
Olson, L., and Bathe, K., 1985, “Analysis of Fluid-Structure Interaction. A Direct Symmetric Coupled Formulation Based on the Fluid Velocity Potential,” Comput. Struct., 21, pp. 21–32. [CrossRef]
Sandberg, G., and Ohayon, R., eds., 2008, Computational Aspects of Structural Acoustics and Vibrations, CISM Courses and Lectures, Vol. 505, Springer, Wien.
Zienkiewicz, O., and Taylor, R., 1991, The Finite Element Method, Vol. 2, McGraw-Hill, London.
Ihlenburg, F., 2008, “Sound in Vibrating Cabins: Physical Effects, Mathematical Formulation, Computational Simulation With Fem,” Computational Aspects of Structural Acoustics and Vibrations, G.Sandberg and R.Ohayon, eds., Springer, Wien, pp. 103–170.
Sandberg, G., Wernberg, P.-A., and Davidson, P., 2008, “ Fundamentals of Fluid-Structure Interaction,” Computational Aspects of Structural Acoustics and Vibrations, G.Sandberg and R.Ohayon, eds., Springer, Wien, pp. 23–101.
ANSYS, 2007, ANSYS, Inc., “ Theory Reference for ANSYS and ANSYS Workbench,” Release 11.0, ANSYS, Inc., Canonsburg, PA.
Harris, C., and Piersol, A., eds., 2002, Harris Shock and Vibration Handbook, 5th ed., McGraw-Hill, New York.
Bermudez, A., and Rodriguez, R., 2002, “Analysis of a Finite Element Method for Pressure/Potential Formulation of Elastoacoustic Spectral Problems,” Math. Comp., 71, pp. 537–552. [CrossRef]
Kropp, A., and Heiserer, D., 2003, “Efficient Broadband Vibro–Acoustic Analysis of Passenger Car Bodies Using an FE–Based Component Mode Synthesis Approach,” J. Comput. Acoust., 11, pp. 139–157. [CrossRef]
Stammberger, M., and Voss, H., 2010, “On an Unsymmetric Eigenvalue Problem Governing Free Vibrations of Fluid-Solid Structures,” Electron Trans. Numer. Anal., 36, pp. 113–125.
Stammberger, M., and Voss, H., 2011, “Automated Multi-Level Sub-Structuring for Fluid-Solid Interaction Problems,” Numer. Linear Algebra Appl., 18, pp. 411–427. [CrossRef]
Ma, Z. D., and Hagiwara, I., 1991, “Improved Mode–Superposition Technique for Modal Frequency Response Analysis of Coupled Acoustic–Structural Systems,” AIAA J., 29, pp. 1720–1726. [CrossRef]
Stammberger, M., 2010, “ On an Unsymmetric Eigenvalue Problem Governing Free Vibrations of Fluid-Solid Structures,” Ph.D. thesis, Institute of Numerical Simulation, Hamburg University of Technology, Hamburg, Germany.
Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., and van der Vorst, H., eds., 2000, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, SIAM, Philadelphia.
Voss, H., 2004, “An Arnoldi Method for Nonlinear Eigenvalue Problems,” BIT Numer. Math., 44, pp. 387–401. [CrossRef]
Voss, H., 2007, “A New Justification of the Jacobi–Davidson Method for Large Eigenproblems,” Linear Algebra Appl., 424, pp. 448–455. [CrossRef]
Fokkema, D., Sleijpen, G., and van der Vorst, H., 1998, “Jacobi-Davidson Style QR and QZ Algorithms for the Partial Reduction of Matrix Pencils,” SIAM J. Sci. Comput. (USA), 20, pp. 94–125. [CrossRef]
Sleijpen, G., and van der Vorst, H., 1996, “A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems,” SIAM J. Matrix Anal. Appl., 17, pp. 401–425. [CrossRef]
Bennighof, J., 1993, “Adaptive Multi-Level Substructuring Method for Acoustic Radiation and Scattering From Complex Structures,” Computational Methods for Fluid/Structure Interaction, A.Kalinowski, ed., Vol. 178, ASME, New York, pp. 25–38.
Bennighof, J., and Kaplan, M., 1998, “Frequency Window Implementation of Adaptive Multi-Level Substructuring,” ASME J. Vibr. Acoust., 120, pp. 409–418. [CrossRef]
Bennighof, J., and Lehoucq, R., 2004, “An Automated Multilevel Substructuring Method for the Eigenspace Computation in Linear Elastodynamics,” SIAM J. Sci. Comput. (USA), 25, pp. 2084–2106. [CrossRef]
Hurty, W., 1960, “Vibration of Structure Systems by Component-Mode Synthesis,” ASCE J. Eng. Mech. Div., 86, pp. 51–69.
Craig, R., Jr., and Bampton, M., 1968, “Coupling of Substructures for Dynamic Analysis,” AIAA J., 6, pp. 1313–1319. [CrossRef]


Grahic Jump Location
Fig. 1

Fluid–solid structure

Grahic Jump Location
Fig. 2

Arrowhead structure of condensed mass matrix in AMLS

Grahic Jump Location
Fig. 3

Geometry of the numerical example

Grahic Jump Location
Fig. 4

Convergence history: nonlinear Arnoldi

Grahic Jump Location
Fig. 5

Convergence history: Jacobi–Davidson

Grahic Jump Location
Fig. 6

Relative errors for AMLS method




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