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Research Papers

Improving the Patch Transfer Function Approach for Fluid-Structure Modelling in Heavy Fluid

[+] Author and Article Information
L. Maxit

 Laboratoire Vibrations-Acoustique, INSA Lyon,25 bis, av. Jean Capelle, 69621 Villeurbanne Cedex, Francelaurent.maxit@insa-lyon.fr

M. Aucejo, J.-L. Guyader

 Laboratoire Vibrations-Acoustique, INSA Lyon,25 bis, av. Jean Capelle, 69621 Villeurbanne Cedex, France

J. Vib. Acoust 134(5), 051011 (Jun 05, 2012) (14 pages) doi:10.1115/1.4005838 History: Received June 14, 2011; Revised October 17, 2011; Published June 04, 2012; Online June 05, 2012

The vibro-acoustic behavior of elastic structures coupled with cavities filled with a heavy fluid can be modeled by using the Finite Element Method. In order to reduce computing time, the Patch Transfer Function (PTF) approach is used to partition the global problem into different sub-problems. Different types of problem partitioning are studied in this paper. Partitioning outside the near field of structures to reduce the number of patches of the coupling surface for frequencies below the critical frequency is of particular interest. This implies introducing a non- standard modal expansion to compute the PTF accurately enough to guarantee the convergence of the PTF method and reduce computation time in comparison to a direct Finite Element resolution. An application on a submarine structure illustrates the interest of this approach.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Structure-Cavity problem and PTF substructuring

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Figure 2

Mesh of the plate-cavity test case (9856 nodes, 567 CQUAD4 elements, 7938 CHEXA elements)

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Figure 3

Pressure field in the cavity at 100 Hz (upper) and 700 Hz (lower) for the reference test case. Results of direct FEM calculation (MSC/NASTRAN).

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Figure 4

Upper part, Patch size criteria λ/2 for the fluid medium (full line) and for the plate structure (dotted line). Lower part, Zlim parameter defined by Eq. 10. (dash-dotted line symbolised λ/2 = 0.7 m and Zlim  = 0.3 m for the upper part and the lower part respectively).

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Figure 5

Substructuring 1: Subsystem 1: 567 CQUAD4, 567 CHEXA; Subsystem 2: 7371 CHEXA

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Figure 6

Substructuring 2: Subsystem 1: 567 CQUAD4, 2268 CHEXA; Subsystem 2: 5670 CHEXA

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Figure 7

Comparison of the acceleration level of the plate at point (1.85, 0.93) for three calculations: dash-dotted line, PTF results with substructuring 1; dash line, PTF results with substructuring 2; solid line, direct FEM results (reference)

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Figure 8

Comparison of the pressure level in the cavity at point (1.03, 0.93, −0.86) for three calculations: dashed-dotted line, PTF results with substructuring 1; dashed line, PTF results with substructuring 2; solid line, direct FEM results (reference)

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Figure 9

Values of damping parameters η and ζ for each modal order: crosses, values for η; circle, values for ζ. Vertical dotted line, splitting between the 100 normal modes and the 10 residual shapes.

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Figure 10

Comparison of three methods to estimate the patch blocked pressure of patch 1: dashed-dotted line, modal superposition without residual shapes; dashed line, modal superposition with residual shapes; solid line, direct FEM results (reference)

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Figure 11

Comparison of three methods to estimate the input patch acoustic impedance of patch 1: dashed-dotted line, modal superposition without residual shapes; dashed line, modal superposition with residual shapes; solid line, direct FEM results (reference)

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Figure 12

Comparison of three methods to estimate the patch acoustic impedance between patch 1 and patch 3: dashed-dotted line, modal superposition without residual shapes; dashed line, modal superposition with residual shapes; solid line, direct FEM results

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Figure 13

Comparison of the acceleration level of the plate at point (1.85, 0.93) for three calculations: dashed-dotted line, PTF results with PAI estimated by modal superposition without residual shapes; dashed line, PTF results with PAI estimated by modal superposition taking the residual shapes into account; solid line, direct FEM results (reference)

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Figure 14

Comparison of the pressure level in the cavity at point (1.03, 0.93, −0.86) for three calculations: dashed-dotted line, PTF results with PAI estimated by modal superposition without residual shapes; dashed line, PTF results with PAI estimated by modal superposition taking the residual shapes into account; solid line, direct FEM results (reference)

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Figure 15

Iso view and top view of the design of the ballast compartments

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Figure 16

Upper part, Patch size criteria λ/2 for the fluid medium (full line), for the 22 mm thick plate (dash line) and for the 50 mm thick plate (dotted line). Lower part, values of the Zlim parameter for the 22 mm thick plate (dash line) and for the 50 mm thick plate (dotted line) (dashed-dotted line symbolised λ/2 = 0.7 m and Zlim  = 0.3 m for the upper part and the lower part respectively).

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Figure 17

Patch definition

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Figure 18

FE model definitions of PTF subsystems

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Figure 19

Comparison of the acceleration level at point M1 for three calculations: dashed-dotted line, FEM results without considering the coupling with the other subsystems (i.e. FEM results of the blocked subsystem); dashed line, PTF results considering the coupling with the other subsystems; solid line, direct FEM results of the whole problem (reference)

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Figure 20

Comparison of the acceleration level at point M1 for two calculations: dashed line, PTF results; solid line, direct FEM results (reference)

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Figure 21

Comparison of the pressure level at point M2 for two calculations: dashed line, PTF results; solid line, direct FEM results (reference)

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Figure 22

Comparison of the acceleration level at point M3 for two calculations: dashed line, PTF results; solid line, direct FEM results (reference)

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Figure 23

Semi-infinite 2D fluid medium with imposed displacements at the boundary

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