Acoustically Fluid-Structure Interaction Simulation of ... · 3 Introduction The Idealization of a...
Transcript of Acoustically Fluid-Structure Interaction Simulation of ... · 3 Introduction The Idealization of a...
Acoustically Fluid-Structure Interaction Simulation of Differential Phase Sensor
Jin-Hyuk Lee
Department of Mechanical Engineering
American University of Sharjah, UAE
• Introduction
• Acoustically fluid-structure interaction Fluid loading effect
Acoustic radiation damping
Verification of Lumped parameter model vs. FEA (Finite ElementAnalysis) model
• Results• Conclusion• Q & A
2
Outline
3
Introduction
The Idealization of a hearing system of the fly, Ormia ochracea
Hearing system of the fly, Ormia ochracea [1]
[1] Miles, R. N., and et al., Mechanically coupled ears for directional hearing in the parasitoid fly Ormiaochracea, J. Acoust. Soc. Am., 98(6), 3059-70 (1995)
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2-D Sensor (Plane strain)
(a) (b)(a) First (rocking) and (b) second (bending) eigenmode shapes of the hydro-acoustic sensor
y
xz
Three dimensional Finite Element Model with axes
1 23(2) (1) 4(3)5 (4)
Representation of the sensor composed of four beam elements where numbers
and numbers with parenthesis represent nodes and elements
FSI PROBLEM IN FREQUENCY DOMAIN
Acoustic Domain
Acoustics Module: Pressure Acoustics (acpr)
Qqpt
p
cs
0
2
2
2
0
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tiexptxp
,
Qc
pqp
s
2
0
2
0
1
Fluid medium(acoustic medium)
For a time-harmonic wave
Wave equation
Helmholtz equation
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FSI PROBLEM IN FREQUENCY DOMAIN
Boundary & Interface Conditions
Infinite boundary (absorb boundary):
PML
Fluid-structure interaction (FSI) boundary:
To couple the acoustic pressure wave to the sensor,
To couple the sensor back to the acoustic problem,
The equation for the interaction bet’n them
Structural Mechanics Module: Plane Strain (acpn)Acoustics Module: Pressure Acoustics (acpr) +
n
aqpn
0
1
2
2
0t
UnPn
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Fluid domain
Sensor structure
PML
Plane wavePnF s
FSI PROBLEM IN FREQUENCY DOMAIN
Solid Domain
Structural Mechanics Module: Plane Strain (acpn)
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Sensor model with material and boundary conditions
Polysilicon plate
PDMS plate
Pinned
FixedFixed
xy
y
x
Constitutive law D
2
2100
01
01
211
ED
where
x
yzxF
yx
y
yxyF
yx
xyyx
Equilibrium equations
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Acoustic Radiation Damping
Post processing plot of the total acoustic pressure at 5000 Hz
FFF KMC dKdM
Frequency response of the sensor in water.
Rayleigh (proportional) damping
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-180
-160
-140
-120
-100
-80
-60
-40
Frequency in Hertz
Tra
nsfe
r fu
nction in d
B
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000-175
-170
-165
-160
-155
-150
-145
-140
Frequency in Hertz
dB
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Results: Fluid loaded mass & Acoustic Radiation Damping
Comparison of frequency responses by FE and lumped parameter models
for a sensor in water.
Natural
frequencies
1st natural
frequency
2nd natural
frequency
In vacuo 870 Hz 18469 Hz
In water 137 Hz 4300 Hz
Percentage
decrease84 % 74 %
Table : Comparison for in vacuo and in water
natural frequencies of the hydro-sensor
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Results: Validation of Lumped-Parameter Model
Galerkin’s method of Beam formulation
FFFFFFF fuKuCuM
2/
1
i
o espf
2/
2
i
o espf
2
2,
2
1
det
det
MK
MKf
TF
2
4,
2
2
det
det
MK
MKf
TF
fA
j,A fwhere represents a matrix with the j-th column replace by a vector
where
Transfer functions
1 23(2) (1) 4(3)5 (4)
Representation of the sensor
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Conclusion
Acoustically fluid-structure interaction has beenperformed which consists of an underwater sensor in fluidmedium using COMSOL Multiphysics Module.
Simulated results are used to validate the lumpedparameter model of the sensor developed in [2].
Simulated results are used to calculate sound radiationdue to the vibration of the sensor in the fluid domain.
[2] Lee, J., et al., Modeling and Characterization of Bio-Inspired Hydro-Acoustic Sensor, Journalof Acoustics and Vibrations
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Q & A
Thank you!