Modeling of Power and Energy Transduction of Embedded Piezoelectric Wafer Active Sensors for

Structural Health Monitoring

Bin Lin, Victor GiurgiutiuUniversity of South Carolina

SPIE Smart Structure

and Materials + Nondestructive Evaluation and Health Monitoring, Sensors and Smart Structures Technologies for Civil, Mechanical,

and Aerospace Systems,

7-11 March 2010, San Diego, CA

Acknowledgments:NSF CMS-0925466

NIST TIP 70NANB9H9007

2

Outline

PWAS Power and Energy Transduction–

Transmitter

–

Receiver–

Pitch-catch

Methods–

Wave propagation method

–

Normal mode expansion method

Conclusions

Transmitter PWAS

(Wave Exciter)

V1 V2

Receiver PWAS

(Wave Detector)

Lamb waves

3

Transmitter Behavior

TransmitterINPUT

Transmitter PWAS

A’A

Electrical response (7-mm transmitter)–

Active power

–

Reactive power

–

Reactive power is dominant•

capacitive behavior

0 200 400 6000

1000

2000

3000

4000Electrical Reactive Power

frequency (kHz)

Pow

er (m

W)

21 ˆ2active RP Y V

21 ˆ2reactive IP Y V

Piezoelectric transduction:

Elec.→ Mech.

Shear-stress excitation of

structure

PWAS-structure interaction

Ultrasonic guided waves from

transmitter PWAS

4

Transmitter Mechanical Response

Active power converts to mechanical power

Mechanical power at both ends are equal

Mechanical power converts to wave power

Waves contain axial and flexural waves

active A AP P P A AP P

Transmitter PWAS

A’A

A WaveP P

Axial

Flexural

7-mm Transmitter

5

Transmitter Size Effects

Reactive power is dominant

Power rating increases when frequency increases

Power rating increases when transmitter size increases

Wave power is relatively small

Tuning effects–

Maximum wave power output depends on both frequency and transmitter size

Increasing transmitter size and frequency requires more input electrical power

Increasing transmitter size may NOT increase the wave power

6

Receiver Behavior

Ultrasonic guided waves arrive at receiver PWAS

V2

Receiver PWAS

(Wave Detector)

waves Oscilloscope

Shear-stress excitation of

PWAS

Piezoelectric transduction:

Mech. → Elec.

Receiver PWAS OUTPUT V2

Only a small portion of wave power converts to receiver output electrical power

Structure-PWAS interaction

7

Receiver Effects

Sensing –

High resistive load (High Z)

Receiver tuning effects–

Large receiver size may not output high voltage under constant strain axial wave

Power harvesting–

7-mm receiver

Load impedance match–

Maximum power output at 400 kHz and 100 Ω

8

Pitch-catch Energy Transduction

Transmitter PWAS

(Wave Exciter)

V1 V2

Receiver PWAS

(Wave Detector)

Lamb waves

Piezoelectric transduction:

Elec.→ Mech.

PWAS-structure interaction

Shear-stress excitation of

structure

Ultrasonic guided waves from

transmitter PWAS

Transmitter PWAS INPUT V1

Piezoelectric transduction:

Mech. → Elec.

Structure-PWAS interaction

Shear-stress excitation of

PWAS

Receiver PWAS OUTPUT V2

Ultrasonic guided waves arrive at receiver PWAS

Structural transfer function H(i)

9

Pitch-catch Power Transduction

0 100 200 300 400 500 6000

10

20

30

40

50

60

70Electrical Active Power (T)

frequency (kHz)P

ower

(mW

)

7-mm transmitter and receiver

10

0 0ˆ( , ) ( ) ( ) i t

eN x t F H x x H x x l e

0 0ˆ( , ) ( ) ( )

2

i t

ehM x t F H x x H x x l e

Assumptions:–

1-D axial and flexural wave

–

Ideal bonding connection–

Ideal excitation source

–

Fully-resistive external load

Axial waves

Flexural waves

PWAS Modeling

MM

NN

PWAS

BEAM

Transmitter A

(Wave Exciter)

V1 V2

Receiver B(Wave Detector)

Lamb waves

( , ) ( , ) ( , )eAw x t EIw x t M x t

( , ) ( , ) eAu x t EAu x t N

11

PWAS elongation

–

where are frequency dependent structural coefficients

Receiver output voltage

Transmitter

Receiver

In-plane surface displacement

Wave Propagation Method

( ), ( ), ( ), ( )AA AB BA BBC C C C

ˆ ˆ( ( ) ( )) i tA A AA B BAu F C F C e

0 0 0 00 0

( ) ( )( ) ( )

0 0

( ) ( )

( ) ( )ˆ ˆ

( )2 2( ) ( )3 3

A A A B B B

F A F A A F B F B BF F

i x i x l i x i x li x t i x t

A BP i x i x l i x i x l

i x t i x t

F F

e e e ee eiF iFu tEA EAe e e ee e

ˆ ˆ( ( ) ( )) i tB A AB B BBu F C F C e

231 0

231 0

ˆ ˆ ˆ(1 ) ( )(1 )B iB B iB B

e

k YF k u R k uY k Y

2 231 0 31 0

2 231 0 31 0

(1 2 )( ) 1(1 ) (1 )

e

e e

k Y Y k YRY k Y Y k Y

ˆ ˆ( )A iA A ISAF k u u

231 0

231 0

( )ˆ ˆ( ) ( )(1 ) ( ) ( ) ( ) 1

B iA ABB A

e B iA AA iB BB

k Y k CV VY k Y k C R k C

(Receiver ratio of external load)

12

Alternative Approach: Normal Mode Expansion Method

Axial vibrations

Flexural vibrations

Surface displacement of a free-free beam

( , ) ( , ) ( , )eAu x t EAu x t N x t

( , ) ( , ) ( , )eAw x t EIw x t M x t

20 0

2 2 2 2

ˆ ( , ) ( , )( , ) ( ) ( )

2

u w

u w

u wu w

n n i tP n n

n nn n

U x l W x lF hu x t U x W x eA

2( ) cos( ), , , , , 1, 2,...u u u u u u u

un n n n n n n u

n EU x A x A c c nL L

( ) cosh cos (sinh sin )w w w w w w wn n n n n n nW x A x x x x

32

2

0

1 1, , , 1, 2,...12 ( )

w w w

w

n n n wL

n

EI bha a I A nA LW x dx

0x 0 x l

FF

L

V

13

Non-harmonic Excitation

231

231

( )( )( )( ) (1 ) ( ) ( ) ( ) 1

iA ABB

A Y iA AA iB BB

k k CVFRFV r k k C R k C

Convolution

Frequency response function (FRF)

-1( ) ( )* ( )out t frf t in t FRF IN F

Axial wave

Flexural wave

15

Conclusions

A systematic investigation of power and energy transduction in PWAS attached to structure during SHM process

Pitch-catch wave propagation between transmitter PWAS and receiver PWAS

PWAS transmitter: –

Active power, reactive power, power rating were investigated

–

Reactive power dominates the power supply requirements! –

Active electrical power converts to mechanical power

–

Mechanical power becomes axial and flexural waves power

PWAS receiver: –

Sensing optimization

–

Power harvesting optimization

Future power and energy analysis:–

2-D wave propagation

–

multi-mode Lamb waves

16

Thank you.