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)

4

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

11

tiexptxp

,

Qc

pqp

s

2

0

2

0

1

Fluid medium(acoustic medium)

For a time-harmonic wave

Wave equation

Helmholtz equation

5

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

6

Fluid domain

Sensor structure

PML

Plane wavePnF s

FSI PROBLEM IN FREQUENCY DOMAIN

Solid Domain

Structural Mechanics Module: Plane Strain (acpn)

7

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

8

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

9

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

10

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

11

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

12

Q & A

Thank you!