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Melih Papila, [email protected] Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary & Structural Optimization Group Interdisciplinary Microsystems Group

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Page 1: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

Melih Papila, [email protected]

Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum

Volume Displacement

Melih PapilaMultidisciplinary & Structural Optimization Group

Interdisciplinary Microsystems Group

Page 2: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Acknowledgement

Guigin WangQuentin Gallas

Dr. Bhavani SankarDr. Mark SheplakDr. Lou Cattafesta

SPONSOR: NASA Langley Research Center

Page 3: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

3

Melih Papila, [email protected]

Design Problem: Piezoelectric composite

driver

Synthetic Jets Sound

generating/receiving devices MEMS PZT Microphone

Displacement actuators

Maximum volume displacementMaximum natural frequency

Orifice

Cavity

Oscillating Piezo-Composite Diaphragm

Net Flow

Applications

Gallas (2002)

Page 4: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

4

Melih Papila, [email protected]

Volume displacement

Electric field

(Voltage )

PZT layer expands/contra

cts

Plate bends

Lateral deflection

w(r)

rdrrwVol )(2

piezoceramic

shim

V

Page 5: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

5

Melih Papila, [email protected]

Configurations

Outer ring

piezoceramic

shim

V

piezoceramic

shim

V

Inner disc

Bimorph

piezoceramic

shim

Unimorph

piezoceramic

shim

V

Page 6: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

6

Melih Papila, [email protected]

Objective

Investigate trade off between volume displacement and natural frequency via Pareto Optimization

“BEAT THE EXISTING DESIGN”

Find the optimum dimensions of the shim and piezoelectric layers in order to achieve

optimum volume displacement

Page 7: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

7

Melih Papila, [email protected]

Outline

Design problem & objective Analysis tool and verification Optimization of Circular Piezo-composite

plateDesign variablesObjective function and ConstraintsResults

Trade-off via Pareto Optimization: Volume displacement versus Natural Frequency

Concluding Remarks

Page 8: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

8

Melih Papila, [email protected]

Analysis: Natural Frequency

0wP

)(rwCeq

Meq 0w

eqeq

natMC

f2

1

Mass Equivalent

Compliance Equivalent

:

:

wM

wC

eq

eq

20

20

2

2

wM

C

w

eq

eq

Energy Kinetic

Energy Potential

analytic

al

Page 9: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

9

Melih Papila, [email protected]

Analysis: Volume displacement

rdrrwVol P 0)(2

V

P

)(rw

analytic

al

Page 10: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

10

Melih Papila, [email protected]

Analysis: Lateral deflection Classical lamination theory

Each layer is isotropic, linear elastic, constant thickness

Bonding line and electrode layer are neglected

Equilibrium equations Constitutive equations

including piezoelectric effect Boundary and interface

matching conditions

32)3(

21)2(

1)1(

)(

)(

0)(

)(

RrRrw

RrRrw

Rr rw

rw

piezoceramic

shim

(3)

(2)

(1)

R1

R2

R3

Wang et al. (2002)Prasad et al. (2002)

Page 11: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

11

Melih Papila, [email protected]

Analysis: Model verification

Using scanning laser vibrometer

Piezoceramic

(PZT-5A) Shim

(Brass) Elastic Modulus (Pa) 6.301010 8.961010 Poisson’s Ratio 0.33 0.32 Density (kg/m3) 7700 8700

Rel. Dielectric Constant 1750 -

31d (m/V) -1.7510-10 - Allowable stress (Pa) 20106 200106

V10 mm

11.5 mm

0.20 mm0.23 mm

Gallas (2002)

fnat (Hz)3505

3542

Test

Analysis

Page 12: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

12

Melih Papila, [email protected]

Analysis: Model verification

unimorph

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

0 5 10 15 20

r (mm)

w (

mm

)

abaqus

analytical

17.6 mm18.5 mm

0.12 mm0.08 mm

16.9 mm

Page 13: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

13

Melih Papila, [email protected]

Outline

Design problem & objective Analysis tool and verification Optimization of Circular Piezo-composite

plateDesign variablesObjective function and ConstraintsResults

Trade-off via Pareto Optimization: Volume displacement versus Natural Frequency

Concluding Remarks

Page 14: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

14

Melih Papila, [email protected]

Design Variables

R1 : radius of the inner PZT layer(s)

R2 : inner radius of the outer ring PZT layer(s)

ts : thickness of the shim and PZT layer(s)

tp : thickness of the PZT layers

(R3 : radius of the shim – fixed)

Lateral deflection of the composite plate determines volume displacement and operational frequency limit

ts

R1

R2

R3

tp

tp

Page 15: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

15

Melih Papila, [email protected]

Objective Function:Maximum Volume

displacementElectric field

(Voltage )

PZT layer expands/contra

cts

Plate bends

Lateral deflection

w(r)

Large PZT coverageSmall ts

rdrrwVol

P 0)(2

maximize

Page 16: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

16

Melih Papila, [email protected]

Formulation & Implementation

UBxLBthat such

all 0

0lim

natff

Solved by MATLAB

Optimization Toolbox

)(,,, 21

x Maximizex

Volps ttRR

ts

R1

R2

R3

tp

tp

Page 17: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

17

Melih Papila, [email protected]

R3 =11.5 mm, tmin = 0.076 mm

Maximum volume displacement

Parameter

Baseline Design

Inner-outer optimum

(unimorph)

Inner-outer optimum (bimorph)

2R (mm) 11.5 11.5 11.5

1R (mm) 10.0 10.86 10.51

st (mm) 0.150 0.076 0.076

pt (mm) 0.080 0.192 0.105

fnat (Hz) 2114 2114 2114

Vol x1010 (m3) 52.251 131.5 187.4

maxV (V) 94.488 226.5 123.8

Frequency Limit + + + Allowable Stress - - - Variable Bounds - + +

tmin

R1

R2

tp

tp

1.05 1.42

Bimorph/unimorphAmount of PZT

Volume displacement

Page 18: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

R3 =11.5 mm Maximum volume displacement

effect of lower bound, tmin

Parameter

Optimum (bimorph)

0.076

Optimum (bimorph)

0.025

2R (mm) 11.50 11.50

1R (mm) 10.51 11.30

st (mm) 0.076 0.025

pt (mm) 0.105 0.135

fnat (Hz) 2114 2114

Vol x1010 (m3) 187.4 266.1

maxV (V) 123.8 159.1

Frequency Limit + + Strength Limit - - Variable Bounds + +

1.38 1.42

0.025/0.076Amount of PZT

Volume displacement

Page 19: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

19

Melih Papila, [email protected]

Outline

Design problem & objective Analysis tool and verification Optimization of Circular Piezo-composite

plateDesign variablesObjective function and ConstraintsResults

Trade-off via Pareto Optimization: Volume displacement versus Natural Frequency

Concluding Remarks

Page 20: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

20

Melih Papila, [email protected]

Methodology:Pareto

Optimization

In multi-objective optimization problem with conflicting objectives

Pareto optimal points: one objective cannot be improved without deterioration in one of the other objectives,

Construct a Pareto hypersurface

minimized

maxim

ized

Objective 1

maximized

Ob

jecti

ve 2

maxim

ized

Page 21: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

50.0

70.0

90.0

110.0

130.0

150.0

1400 1600 1800 2000 2200 2400 2600

f (Hz.)

Q*1

0^10

(m

^3)

(Hz.) natf

)(m x10 310Vol

R3 =11.5 mm : Pareto frontnatural frequency versus volume

displacement

baseline

Freq. , Vol. -

45% , 15%

Freq. , Vol.

23% , -15%

Page 22: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Analytical solutions allowed numerical optimization

Baseline designs were beaten and substantial improvement is predicted

Bimorph configuration without the outer ring offers the optimum performance

Minimum gauge for the layers is a limiting factor

Pareto optimization was used to understand tradeoff betweenMaximum volume displacementMaximum natural frequency

Concluding Remarks

Page 23: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Prasad et al. (2002), “Two-Port Electroacoustic Model of an Axisymmetric piezoelectric Composite Plate,” 43rd AIAA Structures, Structural Dynamics and Materials Conference, Denver, CO.

Wang et al. (2002), “Analysis of a composite piezoelectric circular plate with initial stresses for MEMS,” ASME International Mchanical Engineering Congress, 2002, New Orleans, LA.

Gallas et al. (2003), “Optimization of Synthetic Jet Actuators,” AIAA Aerospace Sciences Meeting, 2003, Reno, NV.

Relevant work

THANK YOU…

Page 24: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

R3 =11.5 mm Maximum volume displacement

effect of lower bound, tmin

Parameter

Optimum (unimorph)

0.076

Optimum (unimorph)

0.025

2R (mm) 11.50 11.50

1R (mm) 10.86 11.27

st (mm) 0.076 0.044

pt (mm) 0.192 0.224

fnat (Hz) 2114 2114

Vol x1010 (m3) 131.5 149.5

maxV (V) 226.5 264.2

Frequency Limit + + Strength Limit - + Variable Bounds + +

1.21 1.14

0.025/0.076Amount of PZT

Volume displacement

Page 25: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Effect of oppositely polarized outer ring

R1

R2

R3

tpts

Ef Ef

R1=16.89, ts=0.081, tp=0.123

0.000

200.000

400.000

600.000

800.000

1000.000

1200.000

1400.000

16.500 17.000 17.500 18.000 18.500R2 (mm)

Qx1

0^10

(m

^3)

opposite polarization

same polarization

Page 26: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Results: R3 =18.5 mm Maximum volume displacement lower bound on t= 0.076 mm

Parameter

Baseline Design

Inner-outer optimum

(unimorph)

Inner-outer optimum (bimorph)

2R (mm) - 18.50 18.50

1R (mm) 12.50 16.84 16.36

st (mm) 0.100 0.076 0.076

pt (mm) 0.110 0.129 0.076

fnat (Hz) 632 632 673

Vol x1010 (m3) 561.3 995.3 1298.3

maxV (V) 129.9 152.2 90.3

Frequency Limit + + - Strength Limit - - - Variable Bounds - + +

Page 27: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Linear Theory – The piezoelectric term

The piezoelectric effect is added by using the following relation for generalized force resultants:

0P

r rP

N NA B

N N

0P

r rP

M MB D

M M

Where2

3111 12

3112 221

zPr

fPz

dQ QNE dz

dQ QN

23111 12

3112 221

zPr

fPz

dQ QME zdz

dQ QM

Page 28: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Piezoelectric Composite Plate Optimization Problem

Objective functionMaximum volume displacement

Design variablesShim Structural Variables : ThicknessPiezoelectric layer Variables : Radii and

thickness

Constraints Frequency LimitStrength LimitVariable Bounds

Page 29: Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary

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Melih Papila, [email protected]

Configurations

R1

R2

R3

tpts

Ef Ef

VAC

EfT = Ef = VAC /tp

positive

R1

R2

tp

tp

ts

Ef

-Ef

Ef

-Ef

VAC

EfB = -Ef = -VAC /tp

positive

EfT = Ef = VAC /tp