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Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering
8-2009
Finite Element Models of Micro-Perforated PanelsJ Stuart BoltonPurdue University, [email protected]
Kang Hou
Follow this and additional works at: http://docs.lib.purdue.edu/herrick
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Bolton, J Stuart and Hou, Kang, "Finite Element Models of Micro-Perforated Panels" (2009). Publications of the Ray W. HerrickLaboratories. Paper 53.http://docs.lib.purdue.edu/herrick/53
Finite Element Models ofFinite Element Models of Micro-Perforated Panels
Kang HouJ. Stuart BoltonRay W. Herrick LaboratoriesPurdue University
Background
Perforated Absorber Porous Media
Micro-perforated Absorber
“Green”
Environmentally Resistant
2
Outline
Classical Maa Model
Equivalent Fluid Model Equivalent Fluid Model
Finite Element Model Rigid Frame (traditional metal panel)-resistant to environment
Elastic Frame (new flexible thin panel)-light weight, energy efficient
Effect of Shaped Panels Effect of Shaped Panels
Future Work
3
Introduction of the Micro-perforated Panels
Environmentally friendlyGood low frequency performanceAffordable recently!
Classical Maa Model (1998)
L
Affordable recently!
No Flexural MotionNo hole interactionResistive Underestimationt
d
t
Maa Model (1975, 1987, 1998)Classical MPP Model
Analytical~Improved Maa ModelNumerical~Finite Element MethodExperimental~Four Microphone Impedance Tube
MPP Models Validation
4
Improved Maa Model (1987)
P1
d
t tP2
End correction
)82
321(32 2
2 tdxx
dt
cr
Shearing region
jZ1
MPP Impedance Based on Ingard’s semi-empiricalformula for perforated panels
Contribution from hole
)85.011(2 t
dxc
tm
Z1: specific acoustic impedance
mjrc
z
0
1End corrections
From sound radiation based onRayleigh’s theory
29
txc: porosity
r : resistance
m: effective mass per unit area
x: perforation constantAccount for the hole interaction 31
Rayleigh s theory
5
p
Equivalent Fluid Model: Rigid Frame
MPPMPP
Johnson-Allard Model
Equivalent Tortuosity
Software Simulation
Finite Element Model (Axis Symmetric)
Tube center lineTube center line
MPP Rigid Porous Material
lengthcharviscous:yresistivit flow :
porosity :
Finite Element Model (Axis-Symmetric)
2d
y tortuositequivalent :lengthchar thermal:
lengthchar viscous:
Parameters Required
2
2
32d
e 21t
1
)14.11(48.0 2 re Impedance Tube
All the existing models can be obtained from an equivalent fluid model by selecting the
i t t
6
appropriate parameters
Finite Element Models: Porous MediaMPPMPP
Tube center lineTube center line
Air AirMPP Magnified View
Porosity Flow Resistivity Tortuosity Viscous
Char.LenThermal Char.Len Density Young’s
ModulusPoisson’s
Ratio Loss Factor
Rigid × × × × ×Rigid × × × × ×
Limp × × × × × ×
Elastic × × × × × × × × ×
7
Elastic × × × × × × × × ×
Experiment Setup
Tested Material: Brass Sample
Hardware: B&K Type 4206 (2.9cm diameter)
SampleNumber Porosity Flow
Resistivity TortuosityViscous Char.Len
[mm]
Thermal Char.Len
[mm]
B1 3 470170 1.1707 0.1016 0.1016
B2 8 44078 1.2882 0.2032 0.2032
B3 9 17414 1.4199 0.3048 0.3048
B4 12 29385 1.1716 0.2032 0.2032
B5 18 8707 1.2196 0.3048 0.3048
B6 27 5804 1 2601 0 3048 0 3048
Software: COMET/ACOUSTICS
B6 27 5804 1.2601 0.3048 0.3048
8
Results-Low Perforation Rate
Panel Vibration Observation
Maa Model underestimates resistive part of the impedance in low perforation rate casein low perforation rate case
FEM model is acceptable
The highlighted peak comes from the flexural panel vibration
9
Results-High Perforation Rate
Maa model overestimates the
Observation
reactance due to neglect of hole interaction
I d M M d l i th Improved Maa Model gives the best match with experimental results
10
Elastic Frame Model
P t i d i th Y ’ i d M d l
Plexiglass Sample
SampleNumber
Diameter[mm]
Thickness[mm]
BulkDensity
Young’s Modulus
Poisson’s Ratio
Loss Factor
Porosity[%]
P1 0.305 1.6 997 1.76e9 0.4 0.07 5.28
Parameters required in the Yoo’s improved Maa model
P2 0.35 1.6 1024 1.76e9 0.4 0.07 2.81
Parameters required in the elastic porous model
SampleNumber
Porosity[%]
Flow Resistivity Tortuosity
Viscous Char.Len
[mm]
Thermal Char.Len
[mm]
BulkDensity
Young’s Modulus
Poisson’s Ratio
Loss Factor
P1 5.28 119000 1.1206 0.15 0.15 997 1.76e9 0.4 0.07
11
P2 2.81 169000 1.1517 0.18 0.18 1024 1.76e9 0.4 0.07
Results Comparison
12
Vibration Mode Validation in AnsysAbsorption curve changes here
Modal SolutionModal Solution
Mode Frequency [Hz]
1. 971.16
22.1970.6
3.
4. 2889.2
5. 3507.8 No change occurs at this model
13
6. 3526.2No change occurs at this model
Effect of W-Shape Panel
4cm
3.
4cm
3.
4cm
3.
D
2cmD
2cmD
2cmThe change of absorption curves mainly comes from the change of equivalentbacking space thickness.
14
Effect of Curved Panel
Panel Vibration1cm1cm1cm1cm
Cr
3.2cm
1cm
Cr
3.2cm
1cm
Cr
3.2cm
By curving the panel, resonance frequency changes, however, the Helmholtz effect (micro-perforation) dominates.
15
( p )
Comparison Between Flat & Shaped Panels
increasedecreasedecrease
increase
Perforation Effect Panel Vibration Cavity Resonance
Significant Noticeable Not observable
16
Significant Noticeable Not observable
Acoustic & Structural Field Contour-W Shape
Acoustic field contour Disturbed by the panel vibrationDisturbed by the panel vibration
Structural movement (axial) contourLess significant than Helmholtz effect
Structural movement (radial) contourStructural movement (radial) contourNegligible in practice
17
Conclusion
This finite element model can predict the performance of micro-perforated panels
The FEM approach has an advantage when The FEM approach has an advantage when dealing with complex configurations and geometries g
A proper FEM model should be chosen A proper FEM model should be chosen based on the panel material properties
18
Future Work
2-D FEM 3-D FEM
One layer
Absorption
Multiple layers
TransmissionPrediction Prediction
Does this porous media model provide a new view to these pending problem?
MPP Performance in nonlinear range?
Does this porous media model provide a new view to these pending problem?
MPP Performance with biased and grazing flow?
19
Th k !Thank you!
20
